1dir.cloud - 1dir.org - 1dir.cc
1 decimal integer ring cycle of many
Quantum Field Fractal Polarization Math Constants
nemeth braille printable arx calc
ᐱ Y φ Θ P Q Ψ
condensed matter
Complex sets of Y Phi Theta Prime Q Psi Quotient Based Numerals
nu mer numer i call numerical nomenclature & arc ratio constants
Numerical values exist before the nomenclature of numerical nomenclature and it is in the moment numerical value is completed that numerical nomenclature is defined in itself the value it is structured. ⅄ncn ⅄X 1⅄ 2⅄ 3⅄ncn +⅄ 1-⅄ 2-⅄
Here on page 3dir the chevron ^ symbol that signifies where a ratio repeating cycle sequence starts is extracted for SQL web search result display about these basic numeral values that may or may not be blocked in your LAN local area network do to program Api neu lib and guid user data softwares as your device might be limited in what internet information returns to your devices when you query to the world wide web from your location. Many of these numbers are used in multiple practical application ways and anyone able to solve the most basic of division seeking information about these numbers may find many of those fractal quotients here or on 1dir
Other reasons these numerals might not be in your web search results should be consulted with the internet service provider of your area...
The repeating ratio sequence numerals will be bolded where the chevron symbol was extracted from these web search result page values and the bold numbers are repeatable in that ratio to the number n of cn notation with any variable set symbol it is applicable with.
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z φ Θ Ψ ᐱ ᗑ ∘⧊° ∘∇° 2⅄ 3⅄ncn 1⅄ 1-⅄ 2-⅄ ⅄ncn +⅄ ∀
To Begin
1st tier fibonacci 01 to 10 digit value for basic numerical display of decimal precision laws not applicable to standard definition floating point. 9 bold numbers are also prime numbers in the ten digit base logic that phi prime fibonacci scale bases share in common of the ten digit example shown below. 2 - 3- 5 - 13- 89 - 1597 - 28657 - 514229 - 434894437
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 1346296 2178309 3524578 5702887 9227465 14930352 24157817 39088169 63245986 102334155 165780141 269114296 434894437 704008733 1138903170
2nd tier 1st divide 1φn
∈1⅄1Y=(Y2/Y1) → φn21(Yn22/Yn21) = φn variables
∈2⅄1Y where numbers of y dividing previous by the later do not equal φ ratios will be noted theta Θ
∈3⅄1Y where numbers of y have no decimals to apply path variant of cn & do not equal phi ratio σ
(Yn8/Yn7) (Yn9/Yn8) (Yn10/Yn9) (Yn11/Yn10) (Yn12/Yn11) (Yn13/Yn12) (Yn14/Yn13) (Yn15/Yn14) (Yn16/Yn15) (Yn17/Yn16) (Yn18/Yn17) (Yn19/Yn18) (Yn20/Yn19) (Yn21/Yn20) (Yn22/Yn21) (Yn23/Yn22) (Yn24/Yn23) (Yn25/Yn24) (Yn26/Yn25) (Yn27/Yn26) (Yn28/Yn27) (Yn29/Yn28) (Yn30/Yn29) (Yn31/Yn30) (Yn32/Yn31) (Yn33/Yn32) (Yn34/Yn33) (Yn35/Yn34) (Yn36/Yn35) (Yn37/Yn36) (Yn38/Yn37) (Yn39/Yn38) (Yn40/Yn39) (Yn41/Yn40) (Yn42/Yn41) (Yn43/Yn42) (Yn44/Yn43) (Yn45/Yn44) (Yn46/Yn45)
φ denotes ratio phi tier 2nd tier first divide quotient ratios before 3rd tier second divide of (φn2/φn1) variable constants where (Yn22/Yn21)=φn21=1.61803399852 or φn21c2=1.618033998521803399852 . . . and so on that φn21 ≠φn22 and φn21c2≠φn22
1φn=∈1⅄1Y=(Y2/Y1) phi ratios cycle back in remainder and vary per step in the ratios
have not read this anywhere . . .
1φn1=(Yn2/Yn1)=(1/0)=0
1φn2=(Yn3/Yn2)=(1/1)=1
1φn3=(Yn4/Yn3)=(2/1)=2
1φn4=(Yn5/Yn4)=(3/2)=1.5
1φn5=(Yn6/Yn5)=(5/3)=1.6 and 1φn5c2=1.66 and so on for cn
1φn6=(Yn7/Yn6)=(8/5)=1.6
1φn7=(Yn8/Yn7)=(13/8)=1.625
1φn8=(Yn9/Yn8)=(21/13)=1.615384 and 1φn8c2=1.615384615384 and so on for cn
1φn9=(Yn10/Yn9)=(34/21)=1.619047 and 1φn9c2=1.619047619047 and so on for cn
1φn10=(Yn11/Yn10)=(55/34)=1.61762941 and 1φn10c2=1.617629411762941 and so on for cn
1φn11=(Yn12/Yn11)=(89/55)=1.618 and 1φn11c2)=1.61818 and so on for cn
1φn12=(Yn13/Yn12)=(144/89)=1.61797752808988764044943820224719101123595505
and
1φn12c2=1.6179775280898876404494382022471910112359550561797752808988764044943820224719101123595505 and so on for cn
1φn13=(Yn14/Yn13)=(233/144)=1.61805 and 1φn13c2=1.618055 and 1φn13c3=1.6180555 and so on for cn cycles of decimal numbers
1φn14=(Yn15/Yn14)=(377/233)=1.61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832
1φn15=(Yn16/Yn15)=(610/377)=1.61830223896551724135014
1φn16=(Yn17/Yn16)=(987/610)=1.618032786885245901639344262295081967213114754098360655737704918
1φn17=(Yn18/Yn17)=(1597/987)=1.6180344478216818642350572441742654508601925025329280648429584599797365754812563323201418439716312056737588652482269503546099290780141843
1φn18=(Yn19/Yn18)=(2584/1597)=1.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129
1φn19=(Yn20/Yn19)=(4181/2584)=1.618034055731424148606811145510835913312693
1φn20=(Yn21/Yn20)=(6765/4181)=1.61803396316670629036115761779478593637885673283903372398947620186558239655584788327911265247548433389141353743123654628079406840468787371442238722793590050227218368811289165271466156421908634298014828988280315713944032525711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242
1φn21=(Yn22/Yn21)=(10946/6765)=1.61803399852
1φn22=(Yn23/Yn22)=(17711/10946)=1.6180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981
1φn23=(Yn24/Yn23)=(28657/17711)=1.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793292304217717802495624188357517983174298458585060132121280560103890237705381401388967308452374230704082208796792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869
1φn24=(Yn25/Yn24)=(46368/28657)=1.618033988205325051470844819764804410789684893743238999197403775691803049865652371148410510520989636040060020239383047771923090344418466692256691209826569424573402659036186621069895662490839934396482534808249293366367728652685207802631119796210350001744774400669993369857277454025194542345674704260739086436123809191471542729525072408137627804724849077014342045573507345500226820672087099138081446069023275290504937711553896081236696095194891300554838259413057891614614230380011864465924555954915029486687371322887950587988973025787765641902502006490560770492375335869072128973723697525909899849949401542380570192274138953833269358271975433576438566493352409533447325260843772900164008793662979376766584080678368286980493422200509474124995638063998325016575356806364937013644135813239348152283909690477021321143176187318979655930488187877307464144886066231636249432948319782252154796384827441811773737655721115259796908259762012771748612904351467355270963464424049970338835188610112712426283281571692780123530027567435530585895243744983773598073769061660327319677565690756185225250375126496144048574519314652615416826604320061416058903583766618976166381686847890567749589978015842551558083539798304079282548766444498726314687510904840004187458561607984087657465889660466901629619290225773807446697142059531702550860173779530306731339637784834420909376417629200544369613009037931395470565655860697211850507729350594968070628467739121331611822591338939875074152912028474718218934291796070768049691174931081411173535261890637540566004815577345849181700806085773109536936874062183759639878563701713368461457933489199846459852741040583452559584045782880273580626025054960393621104791150504239801793628083888753184213281222737899989531353595980039780856335275848832745925951774435565481383257144851170743622849565551174233171650905537913947726558955926998639075967477405171511323585860348256970373730676623512579823428830652196670970443521652650312314617719928813204452664270509823079875772062672296472066161845273406148584987961056635377045747984785567226157657814844540600900303590745716578846355166277000383850368147398541368601039885542799316048434937362599015947238022123739400495515929790278117039466796943155250026171616010049900547859161810377918135185120563911086296541857137872073140942876086122064417070872736155215130683602610182503402310081306487071221691035349129357574065673308441218550441427923369508322573891195868374219213455700177966988868339323725442300310569843319258819834595386816484628537530097358411557385630038036081934605855462888648497749241023135708552884112084307499040374079631503646578497400286143001709878912656593502460131904944690651498761210175524304707401333007642111874934570959974875248630352095474055204662037198590222284258645357155319817147642809784694838957322818159611962173290993474543741494224796733782321945772411627176606064835816728896953623896430191576229193565272010329064451966360749555082527829151690686394249223575391701852950413511532958788428656174756603971106535924904909795163485361342778378755626897442160728617789719789231252399064800921240883553756499284642495725302718358516243849670237638273371253096974561189238231496667480894720312663572600062811878424119761314861988344907003524444289353386607111700457130892975538262902606692954600970094566772516313640646264438008165544195135568970932058484837910458177757615940258924521059427016086819974177338870084098126112293680427120773284014376941061520745367623966221167603028928359563108490072233660187737725512091286596643054053110932756394598178455525700526921869002337997696897791115608751788393760686743204103709390375824405904316571867257563597026904421258331297763199218341068499842970303939700596712845029137732491188889276616533482220748857172767561154342743483267613497574763583068709215898384338904979586139512161077572669853787905223854555605960149352688697351432459782950064556652824789754684719265798932198066789964057647346198136580940084447080992427679101092228774819415849530655686219771783508392364867222668109013504553861185748682695327494155005757755522210978120529015598283141989740726524060438985239208570331856091007432738946854171755592001954147328750392574240150748508217887427155668772027776808458666294448127857068081097114143141291830966256063091042328226960254039152737551034651219597306068325365530236940363610985099626618278256621418850542624838608367938025613288201835502669504833025089855881634504658547649788882297518930802247269428062951460376173360784450570541229019087831943329727466238615347035628293261681264612485605611194472554698677461004292145025648183689848902536901978574170359772481418152632864570611019995114631678124018564399623128729455281432110828069930557978853334263879680357329797257214642146770422584359842272394179432599364902118156122413371951006734829186586174407649090972537250933454304358446452873643437903479080154935966779495411243326237917437275360295913738353630875527794256202672994381826429842621349059566598038873573646927452280420141675681334403461632410929266845796838468785985972013818613253306347489269637435879540775377743657745053564574100568796454618417838573472450012213420804689953589000942178176361796419722929825173605052866664340300799106675506856963394633073943539100394319014551418501587744704609693966570122483162927033534563980877272568656872666364239103883867815891405241302299612660083051261471891684405206406811599260215654115922811180514359493317514045433925393446627351083504902816065882681369298949645810796663991345918972676832885507903828035035069965453466866734131276825906410301148061555640855637366088564748578008863453955403566318874969466447988275116027497644554559095508950692675437065987367833339149248002233311232857591513417315141152249014202463621453746030638238475765083574693792092682416163590047806818578357818334089402240290330460271486896744250968349792371846320270788986983982971001849460864710192972048714101266706214886415186516383431622291237742959835293296576752625885473008340021635202568307917786230240429912412325086366332833164671807935233974247129846110897860906584778588128554977841365111491084202812576333880029312209931255888613602261227623268311407335031580416652126879994416721917856021216456712147119377464493840946365634923404403810587291063265519768293959591024880482953554105454164776494399274173849321282758139372579125519070384199323027532540042572495376347838224517569878214746833234462783962033709041420944271905642600411766758558118435286317479149945911993579230205534424398925218969187284084167917088320480161915064382175384722755347733538053529678612555396587221272289492968559165299926719475171860278465994346930941829221481662421048958369682800013958195205359946958858219632201556338765397634085912691488990473531772341836200579265101022437798792616114736364588058764001814565376696793104651568552186202324039501692431168649893568761559130404438706075304463132916913843040094915727396447639320235893498970583103604703911784206302125135220016051924486163939002686952577031789789580207279198799595212339044561538193111630666154866175803468611508531946819276267578602086750183201312070349303835014132672645426946295843947377604075792999965104511986600132602854450919496109153086505914785218271277523816170569145409498551837247443905503018459713159088529853089995463586558258017238371078619534494189901245768922078375266078096102173988903234811738842167707715392399762710681508880901699410266252573542240988240220539484244687161949959870188784590152493282618557420525526049481802003001011969152388596154517220923334612834560491328471228670132951809331053494783124541996719824126740412464668318386432634260390131555989810517500087238720033499668492863872701259727117283735213036954321806190459573577136476253620406881390236242453850717102278675367275011341033604354956904072303451163764525246885577694804061834804759744565027741912970652894580730711519000593223296227797745751474334368566144397529399448651289388282095125100324528038524618766793453606448686184876295494992497470077119028509613706947691663467913598771678821928324667620476672366263042188645008200439683148968838329204033918414349024671110025473706249781903199916250828767840318246850682206790661967407614195484523851066057158809365948982796524409393865373207244303311581812471647415989112607739819241372090588686882786055762989845412988100638587430645217573367763548173221202498516941759430505635621314164078584639006176501378371776529294762187249188679903688453083016365983878284537809261262518756324807202428725965732630770841330216003070802945179188330948808319084342394528387479498900792127577904176989915203964127438322224936315734375545242000209372928080399204382873294483023345081480964511288690372334857102976585127543008688976515336566981889241721045468820881460027218480650451896569773528282793034860592525386467529748403531423386956066580591129566946993753707645601423735910946714589803538402484558746554070558676763094531877028300240778867292459085040304288655476846843703109187981993928185085668423072896674459992322992637052029172627979202289144013679031301252748019681055239557525211990089681404194437659210664061136894999476567679799001989042816763792441637296297588721778274069162857242558537181142478277558711658582545276895697386327947796349931953798373870258575566179293017412848518686533831175628991171441532609833548522176082632515615730885996440660222633213525491153993788603133614823603308092263670307429249398052831768852287399239278361307882890742227030045015179537285828942317758313850019192518407369927068430051994277139965802421746868129950797361901106186970024775796489513905851973339847157762501308580800502495027392958090518895906759256028195554314827092856893603657047143804306103220853543636807760756534180130509125170115504065324353561084551767456467878703283665422060927522071396168475416128694559793418710960672785008898349443416966186272115015528492165962940991729769340824231426876504867920577869281501901804096730292773144432424887462051156785427644205604215374952018703981575182328924870014307150085493945632829675123006595247234532574938060508776215235370066650382105593746728547998743762431517604773702760233101859929511114212932267857765990857382140489234741947866140907980598108664549673727187074711239836689116097288620581358830303241790836444847681194821509578811459678263600516453222598318037477754126391457584534319712461178769585092647520675576647939421432808737830198555326796245245489758174268067138918937781344872108036430889485989461562619953240046062044177687824964232124786265135917925812192483511881913668562654848728059461911574833374044736015633178630003140593921205988065743099417245350176222214467669330355585022856544648776913145130334647730048504728338625815682032313221900408277209756778448546602924241895522908887880797012946226052971350804340998708866943504204906305614684021356038664200718847053076037268381198311058380151446417978155424503611683009386886275604564329832152702655546637819729908922776285026346093450116899884844889555780437589419688034337160205185469518791220295215828593362878179851345221062916564888159960917053424992148515196985029835642251456886624559444463830826674111037442858638378057717137174163380674878738179153435460794919216945248979306975608053878633492689395261192727780298007467634434867571622989147503227832641239487734235963289946609903339498202882367309906829047004222354049621383955054611438740970792476532784310988589175419618243361133405450675227693059287434134766374707750287887776110548906026450779914157099487036326203021949261960428516592804550371636947342708587779600097707366437519628712007537425410894371357783438601388840422933314722406392853404054855707157064591548312803154552116411348012701957636877551732560979865303416268276511847018180549254981330913912831070942527131241930418396901280664410091775133475241651254492794081725232927382489444114875946540112363471403147573018808668039222528527061450954391597166486373311930767351781414663084063230624280280559723627734933873050214607251282409184492445126845098928708517988624070907631643228530550999755731583906200928219981156436472764071605541403496527898942666713193984017866489862860732107338521129217992113619708971629968245105907806120668597550336741459329308720382454548626862546672715217922322643682171895173954007746798338974770562166311895871863768014795686917681543776389712810133649719091321492131067452978329901943678682346372614021007083784066720173081620546463342289841923439299298600690930662665317374463481871793977038768887182887252678228705028439822730920891928673622500610671040234497679450047108908818089820986146491258680252643333217015039955333775342848169731653697176955019715950727570925079387235230484698328506124158146351676728199043863628432843633318211955194193390794570262065114980633004152563073594584220260320340579963010782705796140559025717974665875702271696269672331367554175245140803294134068464947482290539833199567295948633841644275395191401751753498272673343336706563841295320515057403077782042781868304428237428900443172697770178315943748473322399413755801374882227727954775447534633771853299368391666957462400111665561642879575670865757057612450710123181072687301531911923788254178734689604634120808179502390340928917890916704470112014516523013574344837212548417489618592316013539449349199148550092473043235509648602435705063335310744320759325819171581114561887147991764664828837631294273650417001081760128415395889311512021495620616254318316641658233590396761698712356492305544893045329238929406427748892068255574554210140628816694001465610496562794430680113061381163415570366751579020832606343999720836095892801060822835607355968873224692047318281746170220190529364553163275988414697979551244024147677705272708238824719963708692466064137906968628956275953519209966151376627002128624768817391911225878493910737341661723139198101685452071047213595282130020588337927905921764315873957497295599678961510276721219946260948459364204208395854416024008095753219108769236137767386676902676483930627769829361063614474648427958264996335973758593013923299717346547091461074083121052447918484140000697909760267997347942910981610077816938269881704295634574449523676588617091810028963255051121889939630805736818229402938200090728268834839655232578427609310116201975084621558432494678438077956520221935303765223156645845692152004745786369822381966011794674948529155180235195589210315106256761000802596224308196950134347628851589489479010363959939979760616952228076909655581533307743308790173430575426597340963813378930104337509160065603517465191750706633632271347314792197368880203789649998255225599330006630142722545974805457654325295739260913563876190808528457270474927591862372195275150922985657954426492654499773179327912900861918553930976724709495062288446103918763303904805108699445161740586942108385385769619988135534075444045084970513312628677112049412011026974212234358097497993509439229507624664130927871026276302474090100150050598457619429807725861046166730641728024566423561433506647590466552674739156227099835991206337020623233415919321631713019506577799490525875004361936001674983424643193635062986355864186760651847716090309522978678856823812681020344069511812122692535855113933768363750567051680217747845203615172558188226262344278884740203091740237987228251387095648532644729036535575950029661164811389887287573716718428307219876469972432564469414104756255016226401926230938339672680322434309243814774749624873503855951425480685347384583173395679938583941096416233381023833618313152109432250410021984157448441916460201695920717451233555501273685312489095159995812541438392015912342534110339533098370380709774226192553302857940468297449139826220469693268660362215165579090623582370799455630386990962068604529434344139302788149492270649405031929371532260878668388177408661060124925847087971525281781065708203929231950308825068918588826464738109362459433995184422654150818299193914226890463063125937816240360121436298286631538542066510800153540147258959416547440415954217119726419373974945039606378895208849495760198206371916111246815786718777262100010468646404019960219143664724151167254074048225564434518616742855148829256377150434448825766828349094462086052273441044073001360924032522594828488676414139651743029626269323376487420176571169347803329029556478347349687685382280071186795547335729490176920124227937327703527933838154726593851415012038943364622954252015214432773842342185155459399099696409254283421153644833722999616149631852601458631398960114457200683951565062637400984052761977876260599504484070209721882960533203056844749973828383989950099452140838189622081864814879436088913703458142862127926859057123913877935582929127263844784869316397389817496597689918693512928778308964650870642425934326691558781449558572076630491677426108804131625780786544299822033011131660676274557699689430156680741180165404613183515371462469902641588442614369961963918065394144537111351502250758976864291447115887915692500959625920368496353421502599713856998290121087343406497539868095055309348501238789824475695292598666992357888125065429040025124751369647904525944795337962801409777715741354642844680182852357190215305161042677181840388037826709006525456258505775203266217678054227588372823393935164183271103046376103569808423770806434727989670935548033639250444917472170848309313605750776424608298147049586488467041211571343825243396028893464075095090204836514638657221621244373102557839271382210280210768747600935199078759116446243500715357504274697281641483756150329762361726628746903025438810761768503332519105279687336427399937188121575880238685138011655092996475555710646613392888299542869107024461737097393307045399029905433227483686359353735561991834455804864431029067941515162089541822242384059741075478940572983913180025822661129915901873887706319572879226715985623058938479254632376033778832396971071640436891509927766339812262274487908713403356945946889067243605401821544474299473078130997662002303102208884391248211606239313256795896290609624175594095683428132742436402973095578741668702236800781658931500157029696060299403287154970862267508811110723383466517779251142827232438845657256516732386502425236416931290784101615661095020413860487838922427330146212094776145444394039850647311302648567540217049935443347175210245315280734201067801933210035942352653801863419059915552919007572320898907771225180584150469344313780228216491607635132777331890986495446138814251317304672505844994242244477789021879470984401716858010259273475939561014760791429668143908992567261053145828244407998045852671249607425759849251491782112572844331227972223191541333705551872142931918902885856858708169033743936908957671773039745960847262448965348780402693931674634469763059636389014900373381721743378581149457375161391632061974386711798164497330495166974910144118365495341452350211117702481069197752730571937048539623826639215549429458770980912168056670272533761384652964371706738318735387514394388805527445301322538995707854974351816310151097463098021425829640227518581847367135429388980004885368321875981435600376871270544718567889171930069442021146665736120319642670202742785357853229577415640157727605820567400635097881843877586628048993265170813413825592350909027462749066545695641553547126356562096520919845064033220504588756673762082562724639704086261646369124472205743797327005618173570157378650940433401961126426353072547719579858324318665596538367589070733154203161531214014027986181386746693652510730362564120459224622256342254946435425899431203545381582161426527549987786579195310046410999057821823638203580277070174826394947133335659699200893324493143036605366926056460899605680985448581498412255295390306033429877516837072966465436019122727431343127333635760896116132184108594758697700387339916948738528108315594793593188400739784345884077188819485640506682485954566074606553372648916495097183934117318630701050354189203336008654081027323167114492096171964964930034546533133265868723174093589698851938444359144362633911435251421991136546044596433681125030533552011724883972502355445440904491049307324562934012632166660850751997766688767142408486582684858847750985797536378546253969361761524234916425306207907317583836409952193181421642181665910597759709669539728513103255749031650207628153679729211013016017028998150539135289807027951285898733293785113584813483616568377708762257040164706703423247374114526991659978364797431692082213769759570087587674913633667166835328192064766025752870153889102139093415221411871445022158634888508915797187423666119970687790068744111386397738772376731688592664968419583347873120005583278082143978783543287852880622535506159053634365076595596189412708936734480231706040408975119517046445894545835223505600725826150678717241860627420874480929615800676972467459957427504623652161775482430121785253166765537216037966290958579055728094357399588233241441881564713682520850054088006420769794465575601074781030812715915832082911679519838084935617824615277244652266461946470321387444603412778727710507031440834700073280524828139721534005653069058170778518337578951041630317199986041804794640053041141780367798443661234602365914087308511009526468227658163799420734898977562201207383885263635411941235998185434623303206895348431447813797675960498307568831350106431238440869595561293924695536867083086156959905084272603552360679764106501029416896395296088215793697874864779983948075513836060997313047422968210210419792720801200404787660955438461806888369333845133824196531388491468053180723732421397913249816798687929650696164985867327354573053704156052622395924207000034895488013399867397145549080503890846913494085214781728722476183829430854590501448162752556094496981540286840911470146910004536413441741982761628921380465505810098754231077921624733921903897826011096765188261157832292284607600237289318491119098300589733747426457759011759779460515755312838050040129811215409847506717381442579474473950518197996998988030847611403845482779076665387165439508671528771329867048190668946505216875458003280175873259587535331681613567365739609868444010189482499912761279966500331507136127298740272882716264786963045678193809540426422863523746379593118609763757546149282897721324632724988658966395645043095927696548836235474753114422305195938165195240255434972258087029347105419269288480999406776703772202254248525665631433855602470600551348710611717904874899675471961475381233206546393551313815123704505007502529922880971490386293052308336532086401228321178071675332379523327633736957811354991799560316851031161670795966081585650975328889974526293750218096800083749171232159681753149317793209338032592385804515476148933942841190634051017203475590606134626792755696688418187528352584010887392260180758627909411313117213944237010154587011899361412569354782426632236451826778797501483058240569494364378685835921415360993823498621628223470705237812750811320096311546916983634016121715462190738737481243675192797571274034267369229158669783996929197054820811669051191680915657605471612520501099207872422095823010084796035872561677775063684265624454757999790627071919600795617126705516976654918519035488711309627665142897023414872456991311023484663433018110758278954531179118539972781519349548103430226471717206965139407474613532470251596468576613043933419408870433053006246292354398576264089053285410196461597515441253445929441323236905468122971699759221132707540914959695711344523153156296890812018006071814914331576927103325540007677007362947970827372020797710855986320968698747251980318944760442474788009910318595805562340789335938863105000523432320200998010957183236207558362703702411278221725930837142757441462818857521722441288341417454723104302613672052203650068046201626129741424433820706982587151481313466168824371008828558467390166451477823917367484384269114003559339777366786474508846006211396866385176396691907736329692570750601947168231147712600760721638692117109257772969954984820462714171057682241686149980807481592630072931569948005722860034197578253131870049202638098893813029975224203510486094148026660152842237498691419199497504972607041909481104093240743971804445685172907143106396342952856195693896779146456363192239243465819869490874829884495934675646438915448232543532121296716334577939072477928603831524583871305440206581289039327214991101650556583033813727884984471507834037059008270230659175768573123495132079422130718498098195903269707226855567575112537948843214572355794395784625047981296018424817671075129985692849914506054367170324876993404752765467425061939491223784764629933349617894406253271452001256237568482395226297239766898140070488885787067732142234009142617859510765258052133859092019401891335450326272812925288760163310883902711379418641169696758209163555152318805178490421188540321736399483546777401681962522245873608542415465680287538821230414907352479324423352060578567191262169801444673203754754510241825731932861081062218655127891963569110514010538437380046759953937955822312175035767875213734864082074187807516488118086331437345151271940538088425166625955263984366821369996859406078794011934256900582754649823777785532330669644414977143455351223086854869665352269951495271661374184317967686778099591722790243221551453397075758104477091112119202987053773947028649195659001291133056495795093694385315978643961335799281152946923962731618801688941619848553582021844575496388316990613113724395435670167847297344453362180270091077223714973653906549883100115155110444219562410580311965662839794814530481208779704784171406637121820148654778937083435111840039082946575007851484803014970164357748543113375440555536169173325888962557141361621942282862825836619325121261820846564539205080783054751020693024391946121366507310604738807272219701992532365565132428377010852496772167358760512265764036710053390096660501797117632690093170952995777645950378616044945388561259029207523467215689011410824580381756638866594549324772306940712565865233625292249712112223889451093973549220085842900512963673796978050738039571483407195449628363052657291412220399902292633562480371287992462574589105628642216561398611159577066685277593607146595945144292842935408451687196845447883588651987298042363122448267439020134696583731723488152981819450745018669086087168929057472868758069581603098719335589908224866524758348745507205918274767072617510555885124053459887636528596852426981191331960777471472938549045608402833513626688069232648218585336915936769375719719440276372265066126949785392748717590815507554873154901071291482011375929092368356771469449000244268416093799071780018843563527235928394458596503472101057333286806015982133510137139267892661478870782007886380291028370031754894092193879331402449663258540670691279617545451373137453327284782077677356317828104826045992253201661025229437833688104128136231985204313082318456223610287189866350280908678507868932547021670098056321317653627385978992916215933279826918379453536657710158076560700701399309069337334682625536518128206022961231112817112747321771294971560177269079108071326377499389328959765502320549952891091181910179013853508741319747356666782984960044666224657151830268346302823044980284049272429074920612764769515301671493875841853648323271800956136371567156366681788044805806609205429737934885019366995847436926405415779739679659420036989217294203859440974282025334124297728303730327668632445824754859196705865931535052517709460166800432704051366158355724604808598248246501727326656663293436158704679484942596922217957218131695571762571099556827302229821684056251526677600586244198625117772272045224552465366228146700631608333042537599888334438357120424329134242942387549289876818927312698468088076211745821265310395365879191820497609659071082109083295529887985483476986425655162787451582510381407683986460550650800851449907526956764490351397564294936664689255679240674180828418885438112852008235335171162368705726349582998918239871584604110688487978504379383745681683358341766409603238301287643507694455106954670761070593572251107931744425445789859371183305998534389503437205569319886938618836584429633248420979167393656000279163904107198939177164392644031126775307952681718253829779809470635446836724011585302020448755975852322294727291761175280036291307533935862093031371043724046480790033848623372997871375231182608088774121506089262658338276860801898314547928952786404717869979411662072094078235684126042502704400321038489723278780053739051540635795791604145583975991904246780891230763862232613323097323516069372230170638936385525351572041735003664026241406986076700282653452908538925916878947552081515859999302090239732002652057089018389922183061730118295704365425550476323411382908189971036744948878110060369194263181770597061799909271731165160344767421572390689883798024915378441567505321561922043479778064696234776843354154307847995254213630177
1φn25=(Yn26/Yn25)=(75025/46368)=1.61803398895790200138026224982746721877156659765355417529330572808833678
1φn26=(Yn27/Yn26)=(121393/75025)=1.61803398867044318560479840053315561479506831056314561812729090303232255914695101632789070309896701099633455514828390536487837387537487504165278240586471176274575141619460179940019993335554815061646117960679773408863712095968010663112295901366211262912362545818060646451182939020326557814061979340219926691102965678107297567477507497500833055648117294235254915028323892035988003998667110963012329223592135954681772742419193602132622459180273242252582472509163612129290236587804065311562812395868043985338220593135621459513495501499500166611129623458847050983005664778407197600799733422192602465844718427190936354548483838720426524491836054648450516494501832722425858047317560813062312562479173608797067644118627124291902699100299900033322225924691769410196601132955681439520159946684438520493168943685438187270909696767744085304898367210929690103298900366544485171609463512162612462512495834721759413528823725424858380539820059980006664445184938353882039320226591136287904031989336887704098633788737087637454181939353548817060979673442185938020659780073308897034321892702432522492502499166944351882705764745084971676107964011996001332889036987670776407864045318227257580806397867377540819726757747417527490836387870709763412195934688437187604131956014661779406864378540486504498500499833388870376541152949016994335221592802399200266577807397534155281572809063645451516161279573475508163945351549483505498167277574141952682439186937687437520826391202932355881372875708097300899700099966677774075308230589
1φn27=(Yn28/Yn27)=(196418/121393)=1.6180339887802426828565073768668704126267577207911494072969611097839249380112527081462687304869308773982025322712182745298328569192622309358859242295684265155321970789089980476633743296565699834422083645679734416317250582817790152644715922664404043066733666685887983656388753882019556317085828672163963325727183610257593106686547000238893511157974512533671628512352442068323544191180710584630085754532798431540533638677683227204204525796380351420592620661817402980402494377764780506289489509279777252395113392040727224798793999654016294185002430123647986292455083901048660136910695015363324079642153995699916799156458774393910686777656042770176204558747209476658456418409628232270394503801701910324318535665153674429332828087286746352755101200233950886789188832964009456887958943266909953621708006227706704669956257774336246735808489781124117535607489723460166566441228077401497615183742060909607638002191230136828317942550229420147784468626691819132898931569365614162266358027233860272009094428838565650408178395788884037794601006647829776016739021195620834809255887901279315940787360061947558755447183939765884359065184977717001804057894606773042926692642903627062515960557857537090277034095870437339879564719547255607819231751418945079205555509790515103836300280905818292652788875800087319697181880339064031698697618478824973433394017776972313065827518884943942401950689084214081536826670401093967526957897078085227319532427734712874712709958564332375013386274332127882167835048149399059253828474458988574300000823770728130946594943695270732249800235598428245450726153896847429423442867381150478198907680014498364815104660071009036764887596484146532337119932780308584514757852594465908248416300775168255171220745842017249759047062021698120978969133310816933431087459738205662599985172126893642961291013485126819503595759228291581886929229856746270378028387139291392419661759739029433328116118721837338232023263285362417931841209954445478734358653299613651528506586046971406918026574843689504337152883609433822378555600405295198240425724712298073200266901715914426696761757267717248935276333890751526035273862578567133195489031492754936446088324697470200093909863006927911823581260863476477226858220819981382781544240606954272486881451154514675475521652813588921931248095030191197185999192704686431672336955178634682395195769113540319458288369181089519165025989966472531365070473585791602481197433130411143970410155445536398309622465875297587175537304457423409916552025240335109932203669074823095236133879218735841440610249355399405237534289456558450652014531315644229897934806784575716886476155956274249750809354740388655029532180603494435428731475455751155338446203652599408532617201980344830426795614244643430840328519766378621502063545673968021220333956653184285749590174062754854069015511602810705724382789781947888263738436318403861837173477877637096043429192787063504485431614673004209468420749137100162282833441796479203907968334253210646412890364353793052317678943596418244874086644205184812962856177868575
1φn28=(Yn29/Yn28)=(317811/196418)=1.6180339887383030068527324379639340589966296367949984217332423708621409443126393711370648311254569336822490810414524127116659369304238919040006516714354081601482552515553564337280697288435886731358633119164231384089034609862639880255373743750572758097526703255302467187324990581311285116435357248317363989043773992200307507458583225569957946827683817165432903298068405135985500310562168436701320652893319349550448533230152022727041309859585170401897993055626266431793420154975613233003085256952010508201895956582390615931330122493865124377602867354315795904652323106843568308403506806911790161797798572432261808999175228339561547312364447250252013562911749432333085562422995855776965451231557189259640155179260556568135303281776619250781496604180879552790477451150098259833620136647354112148581087273060513802197354621266889999898176338217474976835116944475557229989104868189269822521357513058884623608834220896251871009785253897300654726145261635898950198047022167011170055697542995041187671191031371870195195959637100469407080817440356790110885967681169750226557647466118176541864798541885163274241668278874644889979533443981712470343858505839587003227810078506043234326792860124835809345375678400146626072966836033357431599955197588815688989807451455569245181195206142003278721909397305745909234387887057194350823244305511714812288079503915119795538087140689753484914824506918917818122575324053803622885886222240324206539115559673756987648789825779714690099685364885091997678420511358429471840666334042704843751590994715351953486951297742569418281420236434542659023103788858454927756111965298496064515472105407854677269903980286939078903155515278640450467879725890702481442637640134814528200063130670305165514362227494425154517406754981722652710036758341903491533362522783044323839973933142583673594069789937785742650877210846256453074565467523343074463643861560549440478978505024997708967609893186978790131250700037674754859534258571006730544043824904031198769970165667097720168212689264731338268386807726379456057998757751326253194717388426722601798205867079391909091834760561659318392408027777494934272826319380097547067987658972191957967192416173670437536274679510024539502489588530582736816381390707572625726766385972772352839352808805710270952764003299086641753810750542210998991945748353002270667657750308016576892138195073771242961439379282957773727458786872893522996874013583276481788838090195399606960665519453410583551405675650907757944791210581514932440000407294647130100092659532222097771080043580527242920709914569947764461505564663116414992515960858984410797381095418953456404199207811911331955319777209828019835249315235874512519219216161451598122371676730238572839556456129275320999093769410135527293832540805832459346903033326884501420440081866224073150118624565976641651987088759685975827062692828559500656762618497286399413495708132655866570273600179209644737244040770194177723019275219175431986885112362410777016363062448451771222596707022777953140750847681984339520817847651437240986060340701972324328727509698703784785508456455111038703173843537761304972049404840696881141239601258540459632009286317954566282112637334663829180624993636021138592186052194809029722326874319054261829363907584844566180288975552138806015741938111578368581290920384078852243684387377938885438198128481096437190074229449439460741887199747477318779337942551090022299381930372980073109389159852966632386033866549908867822704640104267429665305623720840248857029396491156614974187701738129906627702145424553757802238084085979900009164129560427252084839474997199849300980561862965715973077823824700383875204920119337331609119327149242941074646926452769094482175768004968994694987221130446293109592807176531682432363632660957753362726430367888890020262908694722479609811728049364111232168131230335305318249854901281959901841990041645877669052734474437169709497092934456108910588642588764777158916188943986803653432984756997831156004032217006587990917329368998767933692431447219704915028154242482868168905090164852508425908012503945666894072844647639218401572157337922186357665794377297396368968220835157673940270239998370821411479599629361871111608915679825677891028317160341720208942153977741347534340029936156564062356810475618324186174383203168752354672178720891160687920659002739056501949923123135354193607510513293079045708641774175482898716003624922359457890824669836776670162612387866692461994318239672535103707399525501736093433392051644961256096691749228685761997372949526010854402346017167469376533718905599283161421051023836919223289107922899123298272052459550550356891934547750206192915109613171908888187436996609272062641916728609394251036055758637192110702685089961205184860857966174179555845187304625848954780111802380637212475435041594965838161471962854728181734871549450661344683277500025455915445631255791220763881110692502723782952682544369660621735278844097791444775937032247553686525674836318463684591025262450488244458247207486075614251239703082202242157032451201010090724882648229795639910802472278508079707562443360588133470455864533800364528709181439582930281338777505116639004571882414035373540103249193047480373489191418301784968791047663656080399963343481758290991660642100011200602796077752548137136107688704701198464499180319522650673563522691403028235701412294188923622071296927980124021220051115478214827561628771293873270270545469356168986549094278528444439918948365221110081560753087802543555071327475078658778727000580394872160392632039833416489323789062102251321162011628262175564357645429644940891364335244224052785386268060972008675375983871131973648036330682524004928265230274211121
1φn29=(Yn30/Yn29)=(514229/317811)=1.618033988754322537608830405492572629644663022991652271318488032195235533068395996362
1φn30=(Yn31/Yn30)=(832040/514229)=1.618033988748203621343798191078293911856390 extended shell factoring to divisor 514,229 potential digits long and less
1φn31=(Yn32/Yn31)=(1346296/832040)=1.6180664391135041584539204845920869188981298976010768713042642
1φn32=(Yn33/Yn32)=(2178309/1346296)=1.618001539037477642360966681918389418077451021172164219458425190299904330102741150534503556424441578969260846054656628260055738114055155775550101909238384426604550559460920926750135185724387504679505844182854290586914021879289547023834283099704671186722682084771848092841395948587829125244374194085104612952872176698140676344578012561873466161973295619982529844848384010648475520984983985691111018676427769227569568653550185100453392121791938771265754336342082276111642610540326941474980242086435672392995299696352065221912566033026912358054989393120086518863608002994883740277026745975624974002745310095253941183810989559502516534253982779418493407096210640156399484214466952289838193086810032860529928039599018343662909196788819100702965766815024333430389750842311051952913772305644523938272118464290170957946840813610082775258932656711451270745809242543987354935318830331516991805665321742024042261137223909155193211596855372072709121916725593777297117424399983361756998460962522357639033318081610581922548978827835780541574809700095669897258849465496443575558421030739153945343371739944261885944844224449898090761615573395449440539079073249864814275612495320494155817145709413085978120710452976165716900295328813277317915228151907158604051412170874755625805914895387047127823301859323655421987438126533838026704380017470155151615989351524479015016014308888981323572230772430431346449814899546607878208061228734245663657917723888357389459673058525019757913564327607004700303647934778087433966973087641945010606879913481136391997005116259722973254024375025997254689904746058816189010440497483465746017220581506592903789359843600515785533047710161806913189967139470071960400981656337090803211180899297034233184975666569610249157688948047086227694355476061727881535709829042053159186389917224741067343288548729254190757456012645064681169668483008194334678257975957738862776090844806788403144627927290878083274406222702882575600016638243
1φn33=(Yn34/Yn33)=(3524578/2178309)=1.618033988749989097047296779290725053240839568674600 extended shell factoring to divisor 2,178,309 potential digits long and less
1φn34=(Yn35/Yn34)=(5702887/3524578)=
1.6180339887498588483500719802484155549969386405975410389555856048582269990903875584538063847643604425834809160132078223265310059814252940352008098558182000795556233966165594859866911726737215065179434247163773932652362921178081461099740167475368682435173799530043029264780067287488034028470926164777740767830928979299082046134317356574318968114764377465898045099299831071975141421185741952653622646455831024309860641472539407554606537293258937665729060330059371646761683242646353691136924760921733041515892115311393307227134709460253113989816653227705557941972060201249624777774814460057345872328545431538186982952285351608050665923693559909867223820837558425434193824054964878064834995849148465433308611697627347160426014121406874808842363539691843959759154145545934860854263971459845689327913866567855783018562789644604261843545525166417085960361779481118023207317301532268543922137628958700871423472540542442244149512367154308969754677013815554656472349313875306490592632649922912757215190017074384507875836483119397556246449929608594277102109812862702995933130150616612825705658946971807688750256059023236256936291380131181662031596406718761792191859564464171313558672839698823518730469293061467216784534205229675722880866872573113717443620200772971969977682434606355711236919710671745667140860551248972217383187434070121302465146182039381735912781615274225737095334533666158047857076790469667574387628816839916721945152015361839062718997848820482906038680375352737263865347851572585427248311712778097122549139216099062072111895381518014355193728156959499832320351542794626760990961187410237480912608544909489873681331495571952159946524094515712235620831770498482371506603059997537293826381484535169884167693267108856719868307638531478094682540718349827979406328927888672062300791754360380164660847341156870411152767792342799620266596454951486390711171663671509043068418403564909047267502662730119747669082653299203479111541864018898148941518672590023543244042265485399954264028204227569938869277400017817735910511839999001298878901247184769353948188974680089361052585586132580978488772272879192913307635694259000651992947808219877670461541778902325328025085556341780491168020682192307845081028140106418413778897785777474636679908913918205243294374532213501871713436331952364226298864715151714616615095480934171410024122036737447717145144752080958344516705262303742462218171934342210613582675713234321952869251297602152654871022857204465328898949037303189204494835977526955000002837219094030547770541608101735867386109769736972766668804038384169679320474678103307686764202693201852817557165708916074491754757590837825124029032695545395789226398167383442783788584051764494926768537963977531494550553286095526897120733318995919511498965266196407059228083475525296929164285766976926031995887167201293317951822884895723686637095277789284277436901665958307632857039906621445177266611775934594155669132588355258416752303396321488700207514204537394263937413216560961340620068558562188154156327367418170345499517956475924209933784980783515076131099950121688326942970193878529571483451352190248024018761962425005206297037546055158943850866685316653511427467345026837255410434951361553071034319569605212311942025399920217399075860996692369980179187409102593274996325801273230440637148617508252051734987848190620267163898770292500265279985291856216545640357512303600601263470406953683533177588919865016464382402659268712452951814373238441594993783652964979069834743336649096714557033494506292668228650351900284232608839980275652858299631899194740476732249931764880788565326118474325153252389364060037825804961615262876860719212342583991615450133320925228495439737750164700568408473298079940350305767101763672133231269105124074428201049884553555063897011216661966340367556059193469402578124246363678148135748449885347976410225564592413616608853598927304204928930498913628808895703258659618257845336377858569167713127642514933702701429788190245754243486737986788773010556157361250056035077107103318468196760009283380875667952305212141708879758087351166579374892540326813593003190736593146754022751092471212156462419047046199573395737021566837221363805822994979824535022348774803678624788556247017373427400386656218134483050169410352104564007379039419754648641624614350994643897794289131918771552225543029548501976690542811082631736338364479378807902676575748926538155773542251015582574708234574465368620016353730857992077349401829098405539613536712763911027078986477246354031603216044587465506508864323615479640399503146192253370474422753589224014903344457123661329100959036798164205757398474370548757893852824366491534589389141054617035003906850692480064280035794356090289390673152927811499702943160855001648424293631748254684674307108538951329776217181177434575146301202583685195787978021766010001764750276487000713276880239279709514160276776397060867996111874953540537335249780257381167334075171552452520557070945798333871459221501127227146058336629236180898819660112501411516499280197515844450030613594024589610444143951417730009096124415461936152356395574165190839867921776734689940185747059647991901441817999204443766033834405140133088273262784934820565752836226067347637078821918538900259832524631317564826200469956970735219932712511965971529073835222259232169071020700917953865682643425681031885235622534101954900700168928024858578814258047346377353544168975690139358527460592445393462706741062334270939669940628353238316757353646308863075239078266958484107884688606692772865290539746886010183346772294442058027939798750375222225185539942654127671454568461813017047714648391949334076306440090132776179162441574565806175945035121935165004150851534566691388302372652839573985878593125191157636460308156040240845854454065139145736028540154310672086133432144216981437210355395738156454474833582914039638220518881976792682698467731456077862371041299128576527459457557755850487632845691030245322986184445343527650686124693509407367350077087242784809982925615492124163516880602443753550070391405722897890187137297004066869849383387174294341053028192311249743940976763743063708619868818337968403593281238207808140435535828686441327160301176481269530706938532783215465794770324277119133127426886282556379799227028030022317565393644288763080289328254332859139448751027782616812565929878697534853817960618264087218384725774262904665466333841952142923209530332425612371183160083278054847984638160937281002151179517093961319624647262736134652148427414572751688287221902877450860783900937927888104618481985644806271843040500167679648457205373239009038812589762519087391455090510126318668504428047840053475905484287764379168229501517628493396940002462706173618515464830115832306732891143280131692361468521905317459281650172020593671072111327937699208245639619835339152658843129588847232207657200379733403545048513609288828336328490956931581596435090952732497337269880252330917346700796520888458135981101851058481327409976456755957734514600045735971795772430061130722599982182264089488160000998701121098752815230646051811025319910638947414413867419021511227727120807086692364305740999348007052191780122329538458221097674671974914443658219508831979317807692154918971859893581586221102214222525363320091086081794756705625467786498128286563668047635773701135284848285383384904519065828589975877963262552282854855247919041655483294737696257537781828065657789386417324286765678047130748702397847345128977142795534671101050962696810795505164022473044999997162780905969452229458391898264132613890230263027233331195961615830320679525321896692313235797306798147182442834291083925508245242409162174875970967304454604210773601832616557216211415948235505073231462036022468505449446713904473102879266681004080488501034733803592940771916524474703070835714233023073968004112832798706682048177115104276313362904722210715722563098334041692367142960093378554822733388224065405844330867411644741583247696603678511299792485795462605736062586783439038659379931441437811845843672632581829654500482043524075790066215019216484923868900049878311673057029806121470428516548647809751975981238037574994793702962453944841056149133314683346488572532654973162744589565048638446928965680430394787688057974600079782600924139003307630019820812590897406725003674198726769559362851382491747948265012151809379732836101229707499734720014708143783454359642487696399398736529593046316466822411080134983535617597340731287547048185626761558405006216347035020930165256663350903285442966505493707331771349648099715767391160019724347141700368100805259523267750068235119211434673881525674846747610635939962174195038384737123139280787657416008384549866679074771504560262249835299431591526701920059649694232898236327866768730894875925571798950115446444936102988783338033659632443940806530597421875753636321851864251550114652023589774435407586383391146401072695795071069501086371191104296741340381742154663622141430832286872357485066297298570211809754245756513262013211226989443842638749943964922892896681531803239990716619124332047694787858291120241912648833420625107459673186406996809263406853245977248907528787843537580952953800426604262978433162778636194177005020175464977651225196321375211443752982626572599613343781865516949830589647895435992620960580245351358375385649005356102205710868081228447774456970451498023309457188917368263661635520621192097323424251073461844226457748984417425291765425534631379983646269142007922650598170901594460386463287236088972921013522753645968396783955412534493491135676384520359600496853807746629525577246410775985096655542876338670899040963201835794242601525629451242106147175633508465410610858945382964996093149307519935719964205643909710609326847072188500297056839144998351575706368251745315325692891461048670223782818822565424853698797416314804212021978233989998235249723512999286723119760720290485839723223602939132003888125046459462664750219742618832665924828447547479442929054201666128540778498872772853941663370763819101
1φn35=(Yn36/Yn35)=(9227465/5702887)=1.6180339887499085989254214575880602228309977 extended shell factoring to divisor 5,702,887 potential digits long and less
1φn36=(Yn37/Yn36)=(14930352/9227465)=1.6180339887498895958965978196611962223644305342799999 extended shell factoring to divisor 9,227,465 potential digits long and less
1φn37=(Yn38/Yn37)=(24157817/14930352)=1.6180339887498968544077192553799133469860590024937121375303140877053668928904020481231788774973289310258726652928209596130084541878182108499518296688517457592426488002426198658946553972739557647401749134916577988248368156356929829919616094784637361530391245966605475878934401546594480826707903470728620463871179996292116890479206384417460485861284449288268622199932057864409358868431233235492371512741293708279617252158555940275219231267956709928875086133267320154273656776477875404411094929309101352734349464768144783190644132167814931623849189891839120738747485658744013536988277302504321398450619248628565488610047505912787588665022767045277967994324581228895340176842448188763399550124471278373075196083789585135032315380106242639155459965043021088853096028814324002541936050804428455538087782525154128985036655532300912932260404845110148776130663228837471480913510947364134482562768781338845862441823206847367027917359215643408809115819908331699078494599457534557792073488957259681486411037060613172415492950199700583080693609902834172965245561524604376373711751739007894790424231123284970106531982635104651250017414190904541299495149210145882695866781975401517660132862239282771096086683019931479177450069496017240584816754487770951414943197588375679287400591760997999243420382855005695779978931508111798033964637940217350535339019468529610018571564823120044323134511497116745807466562074356987698615545032026036626597952948463639705212576367924882146114170650497724367114720403109049270908013421250885444629838599920484125223571420151380221980031013334447841551223976501022882782669825868807379759030463581836516647430683482881046608948000690137781078436730761605620550674223889697978989376807726971206037205284912237836053697863251984949852488407507070161507243767595030579319228374521913482013016170013942069148805065011193306092180546044728215382999677435602322035006274466938220880525790684640254965187692828675439132312486671446192293390001789643003728244317347641904223021667540055318186737995192611667829398797831424202188937005637911283002570870398768897076237720316306005377502151322353284102076093048576483662274003988653449027859490519714471567716554840769996581460370123892591413785823669796934459415290409763949302735796182166368214225625758856857494049704923232888280195939117845312689211881943573734899217379469686983937150309651105345674368561437801332480305889640110293447870485571940969643582415203606720055896873697284565025660480074414856394544482273425301694159655445497869038854542746212547433576917677493471017963943515866203288442228287718869588607154071116340726595059513667192843142613114546797021262459183815626048200337138735911919558226088708424288991980899043773381900172212952514448420238183265873436875433345442893777722052366883245619393300305310953151004075456492921265352618612072910270300392113997044409937555390522607906364163416910733249959545494975604058095884142584180198832552641759551281845196951820024069090936369082256064692915478483025718348770343793635943747340987004191193884779139835417142208033675294460572664328342694130721097533400418154910212431696185059803010672487828820110872134829774944354962294258032228577062349233293361067441678535107544684813861052974504552873234334997594162548880294315900924505999590632558428629144175569336878326780239340639792015620261330744245011771993051469918458720866058616702405944615371425938249814873755153260954597721473679923956246979307654635336126033733163156501601569741959198282800030434647488552178809983850347265757699483575470960095247586928961889177160726016372554377820429149962438929772050920165847395962265323684264108441649600759580216193161420440723701624717220330773179359736461672169550992501717307133817072765598560569770893546247268651134280022333030058500965014086740888627408114691468761084802287313788717104593381321485253663142034427587507648848466533140009023229994845399492255775349435833796818722023432535281150772600672777172299755558341826100282163474779429178896786894240671619798381176813513840798930929424838744592223947566674918314049126236273598907781946467169695664241539650237315235434502816812356466880352184596853443240989897625990331641209798670520293158527005927254762647257077395094234884750205487452673587334042760679721415811228027309737908389567774423536698933822859635191454293910820053003438900837702955697226696329731542833015591326982779776391072360517689067210203751391795719216800782727694564736317000429728649398219144464912816523012987235665977600528105432477412454843663431377907232193855844791870948521508401141513609324147213675873147531953700756686781396714558370760448246632095479061712677638142757786286619364365957346484530304442922712070016835503945251927081156559470265670896439682065097996349985586408143625816725553422986946322497955841898436152074646331178260231239022361964406465433634786373422408259363208583427905785476457621360835966894819358579087753590806164516415955899767132081011887730443327792941519396193740107400013074038709871006390204330078755008589214775378370181761287342723065069062002021117787443993282944702174469831655676972652754603508343272817680386905814410805585829456666527353139430336270705472985499605099732410863454525385603768752404497897973202507214833247066110698528741988132630764499055347121085959661232367461932578682672719303603826621100426835214601772282394949563144927862383954510918429786518094148081706312081590574689732700206934170071810765077742306410458373653883043078957549024966055723267609497753301462684871729748903441794272499402559296659583109627957867302793664878095305455624890826418559991083934256874854658483604405308059716207628594422958011974533487221198803618293795082661145564418039172820573821702261272875549082834751652204850897018369024387368763978237083760650787067846759406610105374608716525906422032112839670491358810562537306555130113476226146577120217929222298308840943602669247181848090386616470931160899622460341189544626945165124037263153608166773295097128319546652349522636840712127885531432882493326346224121172762705125773324031476284015273049155170621563376402646099703476515490056764904136218623646649456087840393850057922278054797368474634757439074443790742508950894124934227940506694014983705675525935356380077308291190991344343388555072244780297209335720952861660595811806714269027280803560425099153723904165152971611118076787472927630909170795169464189457823901271718175164256006824219549545784319083702782091138909518007345037812906219491677088390146461382826071347815510310808479264253113389423102683714355830324696966287198051325246718898522955118539737040359128840364915709957809434097735940853906190557329123921525761750292290496566993196141658281063969556779371310200857956999272354730819474316479611465288963046551079304761200539679171663199903123516444890247731600701711520264224179041458634063014723296543845717770083384504263529754690311387166223542485803415753359331380800666990302706861834201899593525993225076006245532590256411905091052106474113939175714008618149123342838802460919876503916317579116687938770633137115588433547983329529002397264310982085352039925113620897886399463321427384967213097186188242581286764036105779689588028467111826968312602408838050167872800319778127133238385806309188155778242870630243680791986685913366275624312139459270618669941606199237633513262111971640052424751941548330541704576020712706572490722254907318996899738197733047419109743695259160668147676625440579029884894877227275016690832205429583977658396801361414653854108730993080404266423189486758249236186795863888540605070798062898985904685971234971553249380858535686231644103233466967155228490259305
1φn38=(Yn39/Yn38)=(39088169/24157817)=1.618033988749894081903178586045254006187727972274978322751596305245627119370926603177762295326601737234784086658161207198481551540853215338124301545955083607099101711052782625185048798076415596657595344811164021980959620647842476826445038473468029002786137505719163283669215641462968280619064214287242924308930728302147499502955916919148779047378328927651037343316244178851094037180594587664936778020961082700477447941591742333340798135858053730599913063336807295129357093813567674595763350637187126634827973073891568927771909191960515306494788001747012157596855709272075370055166822399557046069187460108667931378071122899887849965913724737628404089657604410199812342315532897695184958144189932393311862574337739208803510681449404141110929021442624555024984252509239555875433612234085554998615975938554381796997634347507475530591195388225682809005466015410250023832865361965445801663287705176341057637782420489401008377536761703261515723875216042906525866968857326802334830171120180271255469813352754514201345262280942023859192244067417184259653924855875843417474352090671106582188282989311492838943187623285663601144093441886740014629633132828185593093945533240855330595475576290688848251479014018526591206481943298105122660710609737626541338565483793506673222998584681720206755436552897142982745502211561582737380616799936848598530239714954376879334751149079405643316198644935508866550317853637189154963794948856512987079917030582688824904998659440130703862853170880464902933903340686784737213631513145413759860835107741730140600038488577010083320028461180908854471411882952834687008350133623414731554593695282980246104190622853050008616258662775696992820170796061581226482508746547753052355682634734752730348110510150813709699017920369212168467043193513718561573671991968479602275321482897233636631985414907315507854041613114297537728678050669892896365594623057207528312678252343744469957695266919192243239527809983824283460711702551600585433692125410172616176370571893975353816116745979158630103042837024553998401428407210800545430077560402084343962039285254954948950892375747361609701737536963708268839026307716462956897140167921629673740801993822537855966041964801703730101109715335619936188770698941878730184933514481047687380031068204548449058952636324714273644841336450226442231928489233940301807899281627971600248482716795147508568344565239483352324425671408968782237236088012422645638883678935062716966520609043441301008282329483661541106963431339843331042701416274492020533146682914271599954581988927227985873061295232098165161198133092903220518642061076959064637338713179257877481231023481964450678635408157947384070340461640221879319642167998871752360736899364706670308827987230799869044458777049267324112936197836087590199064758210561823529005124924988048382020610554339409061671425029836098187183055488829971681630008208109201257712979612354874614705459520618108829949328616902760708883588281176233763174876272967876195104880544463102771247915322812487568723614389495540925738447310864222541299985838952253011933983935717370489229221332374527052672019164645547236325202728375664075938649589075039354756267919406790770871391235391840247817093738229741536662853270227189816033460308106481641118483511982891500502715125294640653996178545437280197958284061842177213280488050720808092883558146003010122975929488993148677299774230428188109877643331762965171894463808546939485467581776946153702546881616000319896454220180573435091424030573623436256678324866853656520371853135570983090069769135183034129284115365225260212874366918169799862297160376701255746742348449779216391944686061658634139003536619223500202853593931935157882850093615660719675126274861673138760840849154540743478601564040326988154600227330143282400061230698121440360277586339858440023781950165447482278717485110513089820988378213147322044868540895065145993944734327609154419871629957292912683294190033809760211363468810116410766750985819621036122593361809140287800011068880934067842305453344563376732260203808978269849465289020113034219938001848428605945644840342982977311236358815036971262759379293253194193829682541266042374606943996636782205941869664796285194146474410332688586886803555139108802753162671941756989052446253732280528493116741467161540299771291420909430682416378930265098042592176271556324811964591005884347911071600550662338405825327677579476655527277154222999536754500623959524157335904978500333867087411085198633634818907685243248593198632144
1φn39=(Yn40/Yn39)=(63245986/39088169)
1φn40=(Yn41/Yn40)=(102334155/63245986)
1φn41=(Yn42/Yn41)=(165780141/102334155)
1φn42=(Yn43/Yn42)=(269114296/165780141)
1φn43=(Yn44/Yn43)=(434894437/269114296)
1φn44=(Yn45/Yn44)=(704008733/434894437)
1φn45=(Yn46/Yn45)=(1138903170/704008733)
1⅄1Y=(Y2/Y1) → 1φn
NOTE: forward progress past this phase of phi base radicals math is based on the same division properties of dividing the later by the previous. Numerals of the Y function past 1φn24 will continue to differ φ ratios from one another and in progression will extend the precision of the golden ratio to the extent of each ratio later provided than the previous. NOTE ALT PATH: variables Θ=2⅄(Y1/Y2)
With path variable set ratios 1φn Y can be again divided with 1φn in 1⅄ 2⅄ 3⅄ for (1φn/Yn) and (Yn/1φn) functions as with P variables (ᐱ)R,Z. More complex ratio sets (ᐱ)D,B,O,G, that require factoring and definitions of Θ variables and (ᐱ)A,M,V,W then require definition of Q and the path of Q from Prime P paths 1⅄ and 2⅄ for D, B, O, G, A, M, V, W, R, and Z variables.
D=∈1⅄(φ/Θ)cn
B=∈2⅄(φ/Θ)cn
O=∈1⅄(Θ/φ)cn
G=∈2⅄(Θ/φ)cn
A=∈1⅄(φ/Q)cn
M=∈2⅄(φ/Q)cn
V= ∈1⅄(Q/φ)cn
W=∈2⅄(Q/φ)cn
R=∈(φ/P)cn
Z=∈(P/φ)cn
Alternate Path of φn 3rd tier 2nd divide 1⅄2φn from Y base numeral ratios 1φn
Later φ divided by Previous φ of ordinal ratios from Y base
3rd tier 2nd divide 1⅄2φn
[(φn2/φn1)] = [(Yn3/Yn2) / (Yn2/Yn1)] = [(2/1)/(1/0)] = (2/0)=0 . . . and so on →
∈1⅄2φn1=(1φn2/1φn1)=(2/0)=0
∈1⅄2φn2=(1φn3/1φn2)=(2/1)=2
∈1⅄2φn3=(1φn4/1φn3)=(1.5/2)=0.75
∈1⅄2φn4=(1φn5/1φn4)=(1.6/1.5)=1.06 and 1⅄2φn4=(1φn5c2/1φn4)=(1.66/1.5)=1.106 and 1⅄2φn4=(1φn5c3/1φn4)=(1.666/1.5)=1.1106
and so on for cn
∈1⅄2φn5=(1φn6/1φn5)=(1.6/1.^6)=0.^963855421686746987951807228915662650602409 and
∈1⅄2φn5=(1φn6/1φn5c2)=(1.6/1.66)=0.960384143661464585834333733493397358943577430972388955582232893157262905162064825930372148859543817527010804321728691476590636260504201680672268907563025210084033613445378151 and
∈1⅄2φn5=(1φn6/1φn5c3)=(1.6/1.666)=0.960038401536061442457698307932317292691707668306732269290771630865234609384375375015000600024000
and so on for cn variable of 1φn5 then
∈1⅄2φn6=(1φn7/1φn6)=(1.625/1.6)=1.015625
then
∈1⅄2φn7=(1φn8/1φn7)=(1.615384/1.625)=0.9940824061538 and
∈1⅄2φn7=(1φn8c2/1φn7)=(1.615384615384/1.625)=0.994082840236307692
∈1⅄2φn7=(1φn8c3/1φn7)=(1.615384615384615384/1.625)=0.994082840236686390153846
and so on for cn variable of 1φn8 then
NEXT factor set ratio will be displayed here with a set of extremely long decimal precision. continue to 4th tier examples and check back later or try it yourself.. it is a constant factor of true math that will not change. root equations 4 stems to 10 loop factors
Variants ∈ next set of decimal shift group arrays of potential kinetic precision in variable factor change base examples
∈1⅄2φn8=(1φn9/1φn8)=1.619047 /1.615384
Variants ∈ 1⅄2φn8=(1φn9/1φn8)=1.619047/1.615384=1.002267572292408492346092260416099206133030907821298217637416242825235361994423616923282637441004739430376925857876517286288585252794382388336147937580166697206360840518415435463023033532584202889220148274342199749409428346448893885292908683012850195371502998667809016308196688836833842603368610807089831272316675168257206955126459095800131733380347954418268374578428125077380981859421660732061231261421432922450637124052237734185803499353714039510110289565824596504608192231692278739915710444080169173397780342011589813938976738657805202973410656537392966502082476984048374875571381170049969542845540131634329670220826750791143158530727059324594028416772730199135313956310078594331565497739237233995136760052099067466311415737682185783689822358027564906300917305111354321349821466604844420893112721185798546970875036523823437647023865532901217295701826934029308201641281577631077192791311539547253159620251283905251011524194866359949089506891240720472655418154445011217147130341763939713405605106897183579879459001698667313778024296390208148650723295507445907597440989882281859916899015961529890106624802523734294755921811779737820852503181905974059418689302357829469649321771170198541028015629720239893412959581746507332003412191776073057551640972053703639506024573723647132879860144708626555667259301813067357358993279616487472947608741943711216651892057863641090910891775577819267740673425018447626075286123918523397532722869608712228795134779098963466271796674970161893395007007621717189225595895465096843846416703644458531222297608494327045457922079208411127013762671909589298891161482347231370373855380516335434794455135026718105478325896505103431134640432243974184466355987183233212660277148962723414370824522218865607186897975961133699479504563621405189106738707329031363440519402816915358824898599961371413855776706962555033354298420685112641947673122923094446893122625951476552943448740361424899590437939214453034077346315179548639828053267829816316120501379238620662331681197783313441262263338005081144792817063930310068689549976971419798636113766138577576600981562278071344027178677020448388342243330372221094179464449319790217062939833500888952719601036038489919424731209421413112919281112107090326510600575466885892147006532131059859451375029095249179142544435255022954306839735938947024360771185055689545024588580795649826914219776845629274463533128965001758095907846060131832431174259494955998078475458466841320701455505319382977669705778935534832584698127504048572970884941289501443619597569370502679239115900615581186888071195455693506930899783184679308449260361622932999212571128598525180390544910687754985811432166256444288169252638905766089333260698385027956201126171857589279081630126335286222966180177592448606647088246509808194212645414341110131375326238219519324816885644527864582043650302342972321132312812309642784625822714599129371096903275010771432674831495173902923391589863462805128687668071492598663847110036994299807352307562783833472412751395333864889091386320528122105951279076677743496283236679328258791717634940051405733868850997657522917151587486319042407254250382571574312980690659310727356467564368595943750835714604081729173992066282691917215968463226205038554300401638248243142187863690614739281805440687786928680734735517994483045517350673276446962455985697518360959375603571658503488953710077603839087176795114969567654997201904934059022498675237590566701168267111720804465068367645092436225689990739044091064415643586911842633082907841107748374380333097269751340857653660058537165157015297910589679543687445214264843528845153845772893627769001054857544707636079099458704555696973598867085275080104792420873303189829786601823467361320899550818876502429143782530964773700866171750854162230157040059824784695156074345233083898317675550066114310900689866929473115989758472288941824358790231920088350509847813275357438231405040535253537286985633137384052336781842583559079451077886124908999965333320126979095992033656839488319805061830499744952283791346206227126181762354957087602700039123824428123591728034944013312005071240027139057957736364851948551502800572495456188745214760081813364500329352035046013064385923099956641190310786785061632404431394501596400606295469065002501572443456006992764578180904498248713618557562611738137805004878097094179414925491400205771507010097980680746918379778430391783006393526238962376747572094313178785972870846807941641120625188809598736988852186229404277868296330779554520782674583876031952774077247267525244771521817722597227656086726066371834808318022216389415767396482817707740079139077767267720863893662435680927878448715599510704875506504954859030422487779995344760131337192890359196327312886595385369670617017377911382061478880563383071764979719992274282771155341392511006670859684137022528389534623965571034503251237476661895871198427123210332651555295830564125929190830167941492549140018720007131431288164362157852250610381184907116821758789241443520549911971398036721918751207143317006965526710676842162606538135824051742495901903448344170797779351534991060948975599609752232286564680598883084145936817499739999900952343219940274262961623985380565859263803529068011054956592364416138825195742986473507228002753524858566037425187114345538794490969329893078054505925526066867073092218320845074607647669579989411043198397508913298644637574100028229582182317021835055937164166538730109992422854256325430981116564234893934191498739618505507049716971320750979333706412840539224966942844549655066535263442005120763731719516845530226862467376178048067827835362984912565495263045814493643616626139667063682690926739400662628823858587184223070180217211498937713881033859441470263417243207806936307404307582593367276282771155341392511006670859684137022528389534624584618889378624525190295310588689748072284970927132124621761760671146922341684701594172035875061223833284717441797368303759106193821407170059874308523545485160184822927551591448227313609643279866582806317259549432209307508307622124274971152369962807604755278002010667432635212432461879033096774511818861645218721988084566889388814993834283365441282072250313238214566938882643383864140043481921326446219598559847070417931835402603962896747770189626738905424344923553780401440152929582068412216537987252566572406313297643161006918478826706219697607503850477657324774295152137200814171738732090945558461641318720502369715250367714426167400444723978942468168559302308305641259291908301679353020086864794996112379471382655764821243741413806190978739420410256632478717134749384666432253878953852458610460423032542107635088622890284910522823056313545262302957067793168683111879280715916463206270489531603631087097556989545519826864695948458599411656918726445229121992046473160499299237828281077440410453489696567503454287030204582935079213363509852795658196441217691892454054268211149797199922742827711553414544157921583970127226715133986717709225793990778663153776427152924629685573213551700400647771675341590668225016466672939684929403792630012492388711385032907345869465093148130723097412132347478989515805529830554221163512824195361598232989803043734492851235371899189294929255211144223280656487869138235862185090356224897609484803613258519336578794887159957013316951263600481371611951090267082006507431050449923980923421304160496823046408779584296984494089331081649935866642234911327585267651530533916393872918142064054119639664624634142717765868672711875318809645260829623173189780262772195960836556509164384443574550695066931454069125359666803744496664632062716976273133818336692662549585733175517400196980932205419887779004868192330739935519975436181118545188017214482748374380333053936401499581523612961376366238615709948841885273099151656819678788449062266309434784546584589175081590507272574199075885362242042758873431951783600679466925511209
(1160744/1615384) shell continues... factoring to divisor 1,615,384 potential digits long and less
if ∈1⅄2φn8=(1φn9/1φn8)=1.619047 /1.615384
∈1⅄2φn8=(1φn9c2/1φn8)=1.619047619047/1.615384
and
∈1⅄2φn8=(1φn9/1φn8c2)=1.619047/1.615384615384
then variant cycle differential quotient of two cycle dividend variant remainder shell (1φn9c2/1φn8c1)
1.619047619047/1.615384 =1.002267955512744955998078475457847 ext shell 1281752/1615384
variant differential quotient of three cycle dividend variant remainder shell (1φn9c3/1φn8c1)
1.619047619047619047/1.615384 =1.002267955512509129098715847129845 ext shell 926120/1615384
variant differential quotient of two cycle divisor variant remainder shell (1φn9c1/1φn8c2)
1.619047/1.615384615384 =1.00226719476 ext shell 724470117216/1615384615384
variant differential quotient of three cycle divisor variant remainder shell (1φn9c1/1φn8c3)
1.619047/1.615384615384615384 =1.00226719047 ext shell 1000796461677984752/1615384615384615384
and so on for cn
When combined to the degrees of exponential factoring of these variants the final solution can be very exact and rounded estimations of approximations of similar factoring to an exponential precision will not be exact and will be incorrect. Variable change and no variable change are identification markers of many sciences, engineering, and structure bases.
Next sets of phi radical decimal stem path factoring to the degree of the variant decimal cycles per array of same 3rd tier 2nd divide after the 1.619047 /1.615384 variants description set ∈2φn8 (cn)
∈1⅄2φn9=(1φn10/1φn9)=(1.61762941/1.619047) then 1⅄2φn9=(1φn10c2/1φn9)=(1.617629411762941/1.619047) and
1⅄2φn9=(1φn10/1φn9c2)=(1.61762941/1.619047619047) and 1⅄2φn9=(1φn10c2/1φn9c2)=(1.617629411762941/1.619047619047)
∈1⅄2φn10=(1φn11/1φn10)=(1.618/1.61762941) and so on for cn of 1⅄2φn10=(1φn11cn/1φn10cn)
∈1⅄2φn11=(1φn12/1φn11)=(1.61797752808988764044943820224719101123595505/1.6^18)=
0.99998611130400966653240927209344314662296356613102595797280593325092707045735475896168108776266996291718170580964153275648949320148331273176761433868974042027194066749072929542645241038318912237330037082818294190358467243510506798516687268232385661310259579728059332509270704573547589616810877626699629171817058096415327564894932014833127317676143386897404202719406674907292954264524103831891223733003708281829419035846724351050679851668726823238
and then 1⅄2φn11=(1φn12c2/1φn11)=(1.61797752808988764044943820224719101123595505/1.618)=0.9999861113040096665324092720934431466229635661310259579728059332509270704573547589616810877626699629171817058096415327564894932014833127317676143386897404202719406674907292954264524103831891223733003708281829419035846724351050679851668726823238
and then ∈1⅄2φn11=(1φn12/1φn11c2)=(1.61797752808988764044943820224719101123595505/1.61818)
∈1⅄2φn12=(1φn13/1φn12)=(1.61805/1.61797752808988764044943820224719101123595505 )
∈1⅄2φn13=(1φn14/1φn13)= (1.61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832 /1.61805)
∈1⅄2φn14=(1φn15/1φn14)=(1.61830223896551724135014 /1.61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832)
∈1⅄2φn15=(1φn16/1φn15)=(1.618032786885245901639344262295081967213114754098360655737704918/1.61830223896551724135014)
∈1⅄2φn16=(1φn17/1φn16)=(1.6180344478216818642350572441742654508601925025329280648429584599797365754812563323201418439716312056737588652482269503546099290780141843/1.618032786885245901639344262295081967213114754098360655737704918)
∈1⅄2φn17=(1φn18/1φn17)=(1.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/1.6180344478216818642350572441742654508601925025329280648429584599797365754812563323201418439716312056737588652482269503546099290780141843)
∈1⅄2φn18=(1φn19/1φn18)=(1.618034055731424148606811145510835913312693/1.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129)
∈1⅄2φn19=(1φn20/1φn19)=(1.61803396316670629036115761779478593637885673283903372398947620186558239655584788327911265247548433389141353743123654628079406840468787371442238722793590050227218368811289165271466156421908634298014828988280315713944032525711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242/1.618034055731424148606811145510835913312693)
∈1⅄2φn20=(1φn21/1φn20)=(1.61803399852/1.61803396316670629036115761779478593637885673283903372398947620186558239655584788327911265247548433389141353743123654628079406840468787371442238722793590050227218368811289165271466156421908634298014828988280315713944032525711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242)
∈1⅄2φn21=(1φn22/1φn21)=(1.6180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981/1.61803399852)
∈1⅄2φn22=(1φn23/1φn22)=(1.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793292304217717802495624188357517983174298458585060132121280560103890237705381401388967308452374230704082208796792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869/1.6180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981)
(one example of factorable ratio beyond 1⅄2φn22 precise to a stem cycle numerable decimal of two longer ratios)
∈1⅄2φn23=(1φn24/1φn23)=(1.618033988205325051470844819764804410789684893743238999197403775691803049865652371148410510520989636040060020239383047771923090344418466692256691209826569424573402659036186621069895662490839934396482534808249293366367728652685207802631119796210350001744774400669993369857277454025194542345674704260739086436123809191471542729525072408137627804724849077014342045573507345500226820672087099138081446069023275290504937711553896081236696095194891300554838259413057891614614230380011864465924555954915029486687371322887950587988973025787765641902502006490560770492375335869072128973723697525909899849949401542380570192274138953833269358271975433576438566493352409533447325260843772900164008793662979376766584080678368286980493422200509474124995638063998325016575356806364937013644135813239348152283909690477021321143176187318979655930488187877307464144886066231636249432948319782252154796384827441811773737655721115259796908259762012771748612904351467355270963464424049970338835188610112712426283281571692780123530027567435530585895243744983773598073769061660327319677565690756185225250375126496144048574519314652615416826604320061416058903583766618976166381686847890567749589978015842551558083539798304079282548766444498726314687510904840004187458561607984087657465889660466901629619290225773807446697142059531702550860173779530306731339637784834420909376417629200544369613009037931395470565655860697211850507729350594968070628467739121331611822591338939875074152912028474718218934291796070768049691174931081411173535261890637540566004815577345849181700806085773109536936874062183759639878563701713368461457933489199846459852741040583452559584045782880273580626025054960393621104791150504239801793628083888753184213281222737899989531353595980039780856335275848832745925951774435565481383257144851170743622849565551174233171650905537913947726558955926998639075967477405171511323585860348256970373730676623512579823428830652196670970443521652650312314617719928813204452664270509823079875772062672296472066161845273406148584987961056635377045747984785567226157657814844540600900303590745716578846355166277000383850368147398541368601039885542799316048434937362599015947238022123739400495515929790278117039466796943155250026171616010049900547859161810377918135185120563911086296541857137872073140942876086122064417070872736155215130683602610182503402310081306487071221691035349129357574065673308441218550441427923369508322573891195868374219213455700177966988868339323725442300310569843319258819834595386816484628537530097358411557385630038036081934605855462888648497749241023135708552884112084307499040374079631503646578497400286143001709878912656593502460131904944690651498761210175524304707401333007642111874934570959974875248630352095474055204662037198590222284258645357155319817147642809784694838957322818159611962173290993474543741494224796733782321945772411627176606064835816728896953623896430191576229193565272010329064451966360749555082527829151690686394249223575391701852950413511532958788428656174756603971106535924904909795163485361342778378755626897442160728617789719789231252399064800921240883553756499284642495725302718358516243849670237638273371253096974561189238231496667480894720312663572600062811878424119761314861988344907003524444289353386607111700457130892975538262902606692954600970094566772516313640646264438008165544195135568970932058484837910458177757615940258924521059427016086819974177338870084098126112293680427120773284014376941061520745367623966221167603028928359563108490072233660187737725512091286596643054053110932756394598178455525700526921869002337997696897791115608751788393760686743204103709390375824405904316571867257563597026904421258331297763199218341068499842970303939700596712845029137732491188889276616533482220748857172767561154342743483267613497574763583068709215898384338904979586139512161077572669853787905223854555605960149352688697351432459782950064556652824789754684719265798932198066789964057647346198136580940084447080992427679101092228774819415849530655686219771783508392364867222668109013504553861185748682695327494155005757755522210978120529015598283141989740726524060438985239208570331856091007432738946854171755592001954147328750392574240150748508217887427155668772027776808458666294448127857068081097114143141291830966256063091042328226960254039152737551034651219597306068325365530236940363610985099626618278256621418850542624838608367938025613288201835502669504833025089855881634504658547649788882297518930802247269428062951460376173360784450570541229019087831943329727466238615347035628293261681264612485605611194472554698677461004292145025648183689848902536901978574170359772481418152632864570611019995114631678124018564399623128729455281432110828069930557978853334263879680357329797257214642146770422584359842272394179432599364902118156122413371951006734829186586174407649090972537250933454304358446452873643437903479080154935966779495411243326237917437275360295913738353630875527794256202672994381826429842621349059566598038873573646927452280420141675681334403461632410929266845796838468785985972013818613253306347489269637435879540775377743657745053564574100568796454618417838573472450012213420804689953589000942178176361796419722929825173605052866664340300799106675506856963394633073943539100394319014551418501587744704609693966570122483162927033534563980877272568656872666364239103883867815891405241302299612660083051261471891684405206406811599260215654115922811180514359493317514045433925393446627351083504902816065882681369298949645810796663991345918972676832885507903828035035069965453466866734131276825906410301148061555640855637366088564748578008863453955403566318874969466447988275116027497644554559095508950692675437065987367833339149248002233311232857591513417315141152249014202463621453746030638238475765083574693792092682416163590047806818578357818334089402240290330460271486896744250968349792371846320270788986983982971001849460864710192972048714101266706214886415186516383431622291237742959835293296576752625885473008340021635202568307917786230240429912412325086366332833164671807935233974247129846110897860906584778588128554977841365111491084202812576333880029312209931255888613602261227623268311407335031580416652126879994416721917856021216456712147119377464493840946365634923404403810587291063265519768293959591024880482953554105454164776494399274173849321282758139372579125519070384199323027532540042572495376347838224517569878214746833234462783962033709041420944271905642600411766758558118435286317479149945911993579230205534424398925218969187284084167917088320480161915064382175384722755347733538053529678612555396587221272289492968559165299926719475171860278465994346930941829221481662421048958369682800013958195205359946958858219632201556338765397634085912691488990473531772341836200579265101022437798792616114736364588058764001814565376696793104651568552186202324039501692431168649893568761559130404438706075304463132916913843040094915727396447639320235893498970583103604703911784206302125135220016051924486163939002686952577031789789580207279198799595212339044561538193111630666154866175803468611508531946819276267578602086750183201312070349303835014132672645426946295843947377604075792999965104511986600132602854450919496109153086505914785218271277523816170569145409498551837247443905503018459713159088529853089995463586558258017238371078619534494189901245768922078375266078096102173988903234811738842167707715392399762710681508880901699410266252573542240988240220539484244687161949959870188784590152493282618557420525526049481802003001011969152388596154517220923334612834560491328471228670132951809331053494783124541996719824126740412464668318386432634260390131555989810517500087238720033499668492863872701259727117283735213036954321806190459573577136476253620406881390236242453850717102278675367275011341033604354956904072303451163764525246885577694804061834804759744565027741912970652894580730711519000593223296227797745751474334368566144397529399448651289388282095125100324528038524618766793453606448686184876295494992497470077119028509613706947691663467913598771678821928324667620476672366263042188645008200439683148968838329204033918414349024671110025473706249781903199916250828767840318246850682206790661967407614195484523851066057158809365948982796524409393865373207244303311581812471647415989112607739819241372090588686882786055762989845412988100638587430645217573367763548173221202498516941759430505635621314164078584639006176501378371776529294762187249188679903688453083016365983878284537809261262518756324807202428725965732630770841330216003070802945179188330948808319084342394528387479498900792127577904176989915203964127438322224936315734375545242000209372928080399204382873294483023345081480964511288690372334857102976585127543008688976515336566981889241721045468820881460027218480650451896569773528282793034860592525386467529748403531423386956066580591129566946993753707645601423735910946714589803538402484558746554070558676763094531877028300240778867292459085040304288655476846843703109187981993928185085668423072896674459992322992637052029172627979202289144013679031301252748019681055239557525211990089681404194437659210664061136894999476567679799001989042816763792441637296297588721778274069162857242558537181142478277558711658582545276895697386327947796349931953798373870258575566179293017412848518686533831175628991171441532609833548522176082632515615730885996440660222633213525491153993788603133614823603308092263670307429249398052831768852287399239278361307882890742227030045015179537285828942317758313850019192518407369927068430051994277139965802421746868129950797361901106186970024775796489513905851973339847157762501308580800502495027392958090518895906759256028195554314827092856893603657047143804306103220853543636807760756534180130509125170115504065324353561084551767456467878703283665422060927522071396168475416128694559793418710960672785008898349443416966186272115015528492165962940991729769340824231426876504867920577869281501901804096730292773144432424887462051156785427644205604215374952018703981575182328924870014307150085493945632829675123006595247234532574938060508776215235370066650382105593746728547998743762431517604773702760233101859929511114212932267857765990857382140489234741947866140907980598108664549673727187074711239836689116097288620581358830303241790836444847681194821509578811459678263600516453222598318037477754126391457584534319712461178769585092647520675576647939421432808737830198555326796245245489758174268067138918937781344872108036430889485989461562619953240046062044177687824964232124786265135917925812192483511881913668562654848728059461911574833374044736015633178630003140593921205988065743099417245350176222214467669330355585022856544648776913145130334647730048504728338625815682032313221900408277209756778448546602924241895522908887880797012946226052971350804340998708866943504204906305614684021356038664200718847053076037268381198311058380151446417978155424503611683009386886275604564329832152702655546637819729908922776285026346093450116899884844889555780437589419688034337160205185469518791220295215828593362878179851345221062916564888159960917053424992148515196985029835642251456886624559444463830826674111037442858638378057717137174163380674878738179153435460794919216945248979306975608053878633492689395261192727780298007467634434867571622989147503227832641239487734235963289946609903339498202882367309906829047004222354049621383955054611438740970792476532784310988589175419618243361133405450675227693059287434134766374707750287887776110548906026450779914157099487036326203021949261960428516592804550371636947342708587779600097707366437519628712007537425410894371357783438601388840422933314722406392853404054855707157064591548312803154552116411348012701957636877551732560979865303416268276511847018180549254981330913912831070942527131241930418396901280664410091775133475241651254492794081725232927382489444114875946540112363471403147573018808668039222528527061450954391597166486373311930767351781414663084063230624280280559723627734933873050214607251282409184492445126845098928708517988624070907631643228530550999755731583906200928219981156436472764071605541403496527898942666713193984017866489862860732107338521129217992113619708971629968245105907806120668597550336741459329308720382454548626862546672715217922322643682171895173954007746798338974770562166311895871863768014795686917681543776389712810133649719091321492131067452978329901943678682346372614021007083784066720173081620546463342289841923439299298600690930662665317374463481871793977038768887182887252678228705028439822730920891928673622500610671040234497679450047108908818089820986146491258680252643333217015039955333775342848169731653697176955019715950727570925079387235230484698328506124158146351676728199043863628432843633318211955194193390794570262065114980633004152563073594584220260320340579963010782705796140559025717974665875702271696269672331367554175245140803294134068464947482290539833199567295948633841644275395191401751753498272673343336706563841295320515057403077782042781868304428237428900443172697770178315943748473322399413755801374882227727954775447534633771853299368391666957462400111665561642879575670865757057612450710123181072687301531911923788254178734689604634120808179502390340928917890916704470112014516523013574344837212548417489618592316013539449349199148550092473043235509648602435705063335310744320759325819171581114561887147991764664828837631294273650417001081760128415395889311512021495620616254318316641658233590396761698712356492305544893045329238929406427748892068255574554210140628816694001465610496562794430680113061381163415570366751579020832606343999720836095892801060822835607355968873224692047318281746170220190529364553163275988414697979551244024147677705272708238824719963708692466064137906968628956275953519209966151376627002128624768817391911225878493910737341661723139198101685452071047213595282130020588337927905921764315873957497295599678961510276721219946260948459364204208395854416024008095753219108769236137767386676902676483930627769829361063614474648427958264996335973758593013923299717346547091461074083121052447918484140000697909760267997347942910981610077816938269881704295634574449523676588617091810028963255051121889939630805736818229402938200090728268834839655232578427609310116201975084621558432494678438077956520221935303765223156645845692152004745786369822381966011794674948529155180235195589210315106256761000802596224308196950134347628851589489479010363959939979760616952228076909655581533307743308790173430575426597340963813378930104337509160065603517465191750706633632271347314792197368880203789649998255225599330006630142722545974805457654325295739260913563876190808528457270474927591862372195275150922985657954426492654499773179327912900861918553930976724709495062288446103918763303904805108699445161740586942108385385769619988135534075444045084970513312628677112049412011026974212234358097497993509439229507624664130927871026276302474090100150050598457619429807725861046166730641728024566423561433506647590466552674739156227099835991206337020623233415919321631713019506577799490525875004361936001674983424643193635062986355864186760651847716090309522978678856823812681020344069511812122692535855113933768363750567051680217747845203615172558188226262344278884740203091740237987228251387095648532644729036535575950029661164811389887287573716718428307219876469972432564469414104756255016226401926230938339672680322434309243814774749624873503855951425480685347384583173395679938583941096416233381023833618313152109432250410021984157448441916460201695920717451233555501273685312489095159995812541438392015912342534110339533098370380709774226192553302857940468297449139826220469693268660362215165579090623582370799455630386990962068604529434344139302788149492270649405031929371532260878668388177408661060124925847087971525281781065708203929231950308825068918588826464738109362459433995184422654150818299193914226890463063125937816240360121436298286631538542066510800153540147258959416547440415954217119726419373974945039606378895208849495760198206371916111246815786718777262100010468646404019960219143664724151167254074048225564434518616742855148829256377150434448825766828349094462086052273441044073001360924032522594828488676414139651743029626269323376487420176571169347803329029556478347349687685382280071186795547335729490176920124227937327703527933838154726593851415012038943364622954252015214432773842342185155459399099696409254283421153644833722999616149631852601458631398960114457200683951565062637400984052761977876260599504484070209721882960533203056844749973828383989950099452140838189622081864814879436088913703458142862127926859057123913877935582929127263844784869316397389817496597689918693512928778308964650870642425934326691558781449558572076630491677426108804131625780786544299822033011131660676274557699689430156680741180165404613183515371462469902641588442614369961963918065394144537111351502250758976864291447115887915692500959625920368496353421502599713856998290121087343406497539868095055309348501238789824475695292598666992357888125065429040025124751369647904525944795337962801409777715741354642844680182852357190215305161042677181840388037826709006525456258505775203266217678054227588372823393935164183271103046376103569808423770806434727989670935548033639250444917472170848309313605750776424608298147049586488467041211571343825243396028893464075095090204836514638657221621244373102557839271382210280210768747600935199078759116446243500715357504274697281641483756150329762361726628746903025438810761768503332519105279687336427399937188121575880238685138011655092996475555710646613392888299542869107024461737097393307045399029905433227483686359353735561991834455804864431029067941515162089541822242384059741075478940572983913180025822661129915901873887706319572879226715985623058938479254632376033778832396971071640436891509927766339812262274487908713403356945946889067243605401821544474299473078130997662002303102208884391248211606239313256795896290609624175594095683428132742436402973095578741668702236800781658931500157029696060299403287154970862267508811110723383466517779251142827232438845657256516732386502425236416931290784101615661095020413860487838922427330146212094776145444394039850647311302648567540217049935443347175210245315280734201067801933210035942352653801863419059915552919007572320898907771225180584150469344313780228216491607635132777331890986495446138814251317304672505844994242244477789021879470984401716858010259273475939561014760791429668143908992567261053145828244407998045852671249607425759849251491782112572844331227972223191541333705551872142931918902885856858708169033743936908957671773039745960847262448965348780402693931674634469763059636389014900373381721743378581149457375161391632061974386711798164497330495166974910144118365495341452350211117702481069197752730571937048539623826639215549429458770980912168056670272533761384652964371706738318735387514394388805527445301322538995707854974351816310151097463098021425829640227518581847367135429388980004885368321875981435600376871270544718567889171930069442021146665736120319642670202742785357853229577415640157727605820567400635097881843877586628048993265170813413825592350909027462749066545695641553547126356562096520919845064033220504588756673762082562724639704086261646369124472205743797327005618173570157378650940433401961126426353072547719579858324318665596538367589070733154203161531214014027986181386746693652510730362564120459224622256342254946435425899431203545381582161426527549987786579195310046410999057821823638203580277070174826394947133335659699200893324493143036605366926056460899605680985448581498412255295390306033429877516837072966465436019122727431343127333635760896116132184108594758697700387339916948738528108315594793593188400739784345884077188819485640506682485954566074606553372648916495097183934117318630701050354189203336008654081027323167114492096171964964930034546533133265868723174093589698851938444359144362633911435251421991136546044596433681125030533552011724883972502355445440904491049307324562934012632166660850751997766688767142408486582684858847750985797536378546253969361761524234916425306207907317583836409952193181421642181665910597759709669539728513103255749031650207628153679729211013016017028998150539135289807027951285898733293785113584813483616568377708762257040164706703423247374114526991659978364797431692082213769759570087587674913633667166835328192064766025752870153889102139093415221411871445022158634888508915797187423666119970687790068744111386397738772376731688592664968419583347873120005583278082143978783543287852880622535506159053634365076595596189412708936734480231706040408975119517046445894545835223505600725826150678717241860627420874480929615800676972467459957427504623652161775482430121785253166765537216037966290958579055728094357399588233241441881564713682520850054088006420769794465575601074781030812715915832082911679519838084935617824615277244652266461946470321387444603412778727710507031440834700073280524828139721534005653069058170778518337578951041630317199986041804794640053041141780367798443661234602365914087308511009526468227658163799420734898977562201207383885263635411941235998185434623303206895348431447813797675960498307568831350106431238440869595561293924695536867083086156959905084272603552360679764106501029416896395296088215793697874864779983948075513836060997313047422968210210419792720801200404787660955438461806888369333845133824196531388491468053180723732421397913249816798687929650696164985867327354573053704156052622395924207000034895488013399867397145549080503890846913494085214781728722476183829430854590501448162752556094496981540286840911470146910004536413441741982761628921380465505810098754231077921624733921903897826011096765188261157832292284607600237289318491119098300589733747426457759011759779460515755312838050040129811215409847506717381442579474473950518197996998988030847611403845482779076665387165439508671528771329867048190668946505216875458003280175873259587535331681613567365739609868444010189482499912761279966500331507136127298740272882716264786963045678193809540426422863523746379593118609763757546149282897721324632724988658966395645043095927696548836235474753114422305195938165195240255434972258087029347105419269288480999406776703772202254248525665631433855602470600551348710611717904874899675471961475381233206546393551313815123704505007502529922880971490386293052308336532086401228321178071675332379523327633736957811354991799560316851031161670795966081585650975328889974526293750218096800083749171232159681753149317793209338032592385804515476148933942841190634051017203475590606134626792755696688418187528352584010887392260180758627909411313117213944237010154587011899361412569354782426632236451826778797501483058240569494364378685835921415360993823498621628223470705237812750811320096311546916983634016121715462190738737481243675192797571274034267369229158669783996929197054820811669051191680915657605471612520501099207872422095823010084796035872561677775063684265624454757999790627071919600795617126705516976654918519035488711309627665142897023414872456991311023484663433018110758278954531179118539972781519349548103430226471717206965139407474613532470251596468576613043933419408870433053006246292354398576264089053285410196461597515441253445929441323236905468122971699759221132707540914959695711344523153156296890812018006071814914331576927103325540007677007362947970827372020797710855986320968698747251980318944760442474788009910318595805562340789335938863105000523432320200998010957183236207558362703702411278221725930837142757441462818857521722441288341417454723104302613672052203650068046201626129741424433820706982587151481313466168824371008828558467390166451477823917367484384269114003559339777366786474508846006211396866385176396691907736329692570750601947168231147712600760721638692117109257772969954984820462714171057682241686149980807481592630072931569948005722860034197578253131870049202638098893813029975224203510486094148026660152842237498691419199497504972607041909481104093240743971804445685172907143106396342952856195693896779146456363192239243465819869490874829884495934675646438915448232543532121296716334577939072477928603831524583871305440206581289039327214991101650556583033813727884984471507834037059008270230659175768573123495132079422130718498098195903269707226855567575112537948843214572355794395784625047981296018424817671075129985692849914506054367170324876993404752765467425061939491223784764629933349617894406253271452001256237568482395226297239766898140070488885787067732142234009142617859510765258052133859092019401891335450326272812925288760163310883902711379418641169696758209163555152318805178490421188540321736399483546777401681962522245873608542415465680287538821230414907352479324423352060578567191262169801444673203754754510241825731932861081062218655127891963569110514010538437380046759953937955822312175035767875213734864082074187807516488118086331437345151271940538088425166625955263984366821369996859406078794011934256900582754649823777785532330669644414977143455351223086854869665352269951495271661374184317967686778099591722790243221551453397075758104477091112119202987053773947028649195659001291133056495795093694385315978643961335799281152946923962731618801688941619848553582021844575496388316990613113724395435670167847297344453362180270091077223714973653906549883100115155110444219562410580311965662839794814530481208779704784171406637121820148654778937083435111840039082946575007851484803014970164357748543113375440555536169173325888962557141361621942282862825836619325121261820846564539205080783054751020693024391946121366507310604738807272219701992532365565132428377010852496772167358760512265764036710053390096660501797117632690093170952995777645950378616044945388561259029207523467215689011410824580381756638866594549324772306940712565865233625292249712112223889451093973549220085842900512963673796978050738039571483407195449628363052657291412220399902292633562480371287992462574589105628642216561398611159577066685277593607146595945144292842935408451687196845447883588651987298042363122448267439020134696583731723488152981819450745018669086087168929057472868758069581603098719335589908224866524758348745507205918274767072617510555885124053459887636528596852426981191331960777471472938549045608402833513626688069232648218585336915936769375719719440276372265066126949785392748717590815507554873154901071291482011375929092368356771469449000244268416093799071780018843563527235928394458596503472101057333286806015982133510137139267892661478870782007886380291028370031754894092193879331402449663258540670691279617545451373137453327284782077677356317828104826045992253201661025229437833688104128136231985204313082318456223610287189866350280908678507868932547021670098056321317653627385978992916215933279826918379453536657710158076560700701399309069337334682625536518128206022961231112817112747321771294971560177269079108071326377499389328959765502320549952891091181910179013853508741319747356666782984960044666224657151830268346302823044980284049272429074920612764769515301671493875841853648323271800956136371567156366681788044805806609205429737934885019366995847436926405415779739679659420036989217294203859440974282025334124297728303730327668632445824754859196705865931535052517709460166800432704051366158355724604808598248246501727326656663293436158704679484942596922217957218131695571762571099556827302229821684056251526677600586244198625117772272045224552465366228146700631608333042537599888334438357120424329134242942387549289876818927312698468088076211745821265310395365879191820497609659071082109083295529887985483476986425655162787451582510381407683986460550650800851449907526956764490351397564294936664689255679240674180828418885438112852008235335171162368705726349582998918239871584604110688487978504379383745681683358341766409603238301287643507694455106954670761070593572251107931744425445789859371183305998534389503437205569319886938618836584429633248420979167393656000279163904107198939177164392644031126775307952681718253829779809470635446836724011585302020448755975852322294727291761175280036291307533935862093031371043724046480790033848623372997871375231182608088774121506089262658338276860801898314547928952786404717869979411662072094078235684126042502704400321038489723278780053739051540635795791604145583975991904246780891230763862232613323097323516069372230170638936385525351572041735003664026241406986076700282653452908538925916878947552081515859999302090239732002652057089018389922183061730118295704365425550476323411382908189971036744948878110060369194263181770597061799909271731165160344767421572390689883798024915378441567505321561922043479778064696234776843354154307847995254213630177/1.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793292304217717802495624188357517983174298458585060132121280560103890237705381401388967308452374230704082208796792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869)
∈1⅄2φn24=(1φn25/1φn24)=(1.61803398895790200138026224982746721877156659765355417529330572808833678/1.618033988205325051470844819764804410789684893743238999197403775691803049865652371148410510520989636040060020239383047771923090344418466692256691209826569424573402659036186621069895662490839934396482534808249293366367728652685207802631119796210350001744774400669993369857277454025194542345674704260739086436123809191471542729525072408137627804724849077014342045573507345500226820672087099138081446069023275290504937711553896081236696095194891300554838259413057891614614230380011864465924555954915029486687371322887950587988973025787765641902502006490560770492375335869072128973723697525909899849949401542380570192274138953833269358271975433576438566493352409533447325260843772900164008793662979376766584080678368286980493422200509474124995638063998325016575356806364937013644135813239348152283909690477021321143176187318979655930488187877307464144886066231636249432948319782252154796384827441811773737655721115259796908259762012771748612904351467355270963464424049970338835188610112712426283281571692780123530027567435530585895243744983773598073769061660327319677565690756185225250375126496144048574519314652615416826604320061416058903583766618976166381686847890567749589978015842551558083539798304079282548766444498726314687510904840004187458561607984087657465889660466901629619290225773807446697142059531702550860173779530306731339637784834420909376417629200544369613009037931395470565655860697211850507729350594968070628467739121331611822591338939875074152912028474718218934291796070768049691174931081411173535261890637540566004815577345849181700806085773109536936874062183759639878563701713368461457933489199846459852741040583452559584045782880273580626025054960393621104791150504239801793628083888753184213281222737899989531353595980039780856335275848832745925951774435565481383257144851170743622849565551174233171650905537913947726558955926998639075967477405171511323585860348256970373730676623512579823428830652196670970443521652650312314617719928813204452664270509823079875772062672296472066161845273406148584987961056635377045747984785567226157657814844540600900303590745716578846355166277000383850368147398541368601039885542799316048434937362599015947238022123739400495515929790278117039466796943155250026171616010049900547859161810377918135185120563911086296541857137872073140942876086122064417070872736155215130683602610182503402310081306487071221691035349129357574065673308441218550441427923369508322573891195868374219213455700177966988868339323725442300310569843319258819834595386816484628537530097358411557385630038036081934605855462888648497749241023135708552884112084307499040374079631503646578497400286143001709878912656593502460131904944690651498761210175524304707401333007642111874934570959974875248630352095474055204662037198590222284258645357155319817147642809784694838957322818159611962173290993474543741494224796733782321945772411627176606064835816728896953623896430191576229193565272010329064451966360749555082527829151690686394249223575391701852950413511532958788428656174756603971106535924904909795163485361342778378755626897442160728617789719789231252399064800921240883553756499284642495725302718358516243849670237638273371253096974561189238231496667480894720312663572600062811878424119761314861988344907003524444289353386607111700457130892975538262902606692954600970094566772516313640646264438008165544195135568970932058484837910458177757615940258924521059427016086819974177338870084098126112293680427120773284014376941061520745367623966221167603028928359563108490072233660187737725512091286596643054053110932756394598178455525700526921869002337997696897791115608751788393760686743204103709390375824405904316571867257563597026904421258331297763199218341068499842970303939700596712845029137732491188889276616533482220748857172767561154342743483267613497574763583068709215898384338904979586139512161077572669853787905223854555605960149352688697351432459782950064556652824789754684719265798932198066789964057647346198136580940084447080992427679101092228774819415849530655686219771783508392364867222668109013504553861185748682695327494155005757755522210978120529015598283141989740726524060438985239208570331856091007432738946854171755592001954147328750392574240150748508217887427155668772027776808458666294448127857068081097114143141291830966256063091042328226960254039152737551034651219597306068325365530236940363610985099626618278256621418850542624838608367938025613288201835502669504833025089855881634504658547649788882297518930802247269428062951460376173360784450570541229019087831943329727466238615347035628293261681264612485605611194472554698677461004292145025648183689848902536901978574170359772481418152632864570611019995114631678124018564399623128729455281432110828069930557978853334263879680357329797257214642146770422584359842272394179432599364902118156122413371951006734829186586174407649090972537250933454304358446452873643437903479080154935966779495411243326237917437275360295913738353630875527794256202672994381826429842621349059566598038873573646927452280420141675681334403461632410929266845796838468785985972013818613253306347489269637435879540775377743657745053564574100568796454618417838573472450012213420804689953589000942178176361796419722929825173605052866664340300799106675506856963394633073943539100394319014551418501587744704609693966570122483162927033534563980877272568656872666364239103883867815891405241302299612660083051261471891684405206406811599260215654115922811180514359493317514045433925393446627351083504902816065882681369298949645810796663991345918972676832885507903828035035069965453466866734131276825906410301148061555640855637366088564748578008863453955403566318874969466447988275116027497644554559095508950692675437065987367833339149248002233311232857591513417315141152249014202463621453746030638238475765083574693792092682416163590047806818578357818334089402240290330460271486896744250968349792371846320270788986983982971001849460864710192972048714101266706214886415186516383431622291237742959835293296576752625885473008340021635202568307917786230240429912412325086366332833164671807935233974247129846110897860906584778588128554977841365111491084202812576333880029312209931255888613602261227623268311407335031580416652126879994416721917856021216456712147119377464493840946365634923404403810587291063265519768293959591024880482953554105454164776494399274173849321282758139372579125519070384199323027532540042572495376347838224517569878214746833234462783962033709041420944271905642600411766758558118435286317479149945911993579230205534424398925218969187284084167917088320480161915064382175384722755347733538053529678612555396587221272289492968559165299926719475171860278465994346930941829221481662421048958369682800013958195205359946958858219632201556338765397634085912691488990473531772341836200579265101022437798792616114736364588058764001814565376696793104651568552186202324039501692431168649893568761559130404438706075304463132916913843040094915727396447639320235893498970583103604703911784206302125135220016051924486163939002686952577031789789580207279198799595212339044561538193111630666154866175803468611508531946819276267578602086750183201312070349303835014132672645426946295843947377604075792999965104511986600132602854450919496109153086505914785218271277523816170569145409498551837247443905503018459713159088529853089995463586558258017238371078619534494189901245768922078375266078096102173988903234811738842167707715392399762710681508880901699410266252573542240988240220539484244687161949959870188784590152493282618557420525526049481802003001011969152388596154517220923334612834560491328471228670132951809331053494783124541996719824126740412464668318386432634260390131555989810517500087238720033499668492863872701259727117283735213036954321806190459573577136476253620406881390236242453850717102278675367275011341033604354956904072303451163764525246885577694804061834804759744565027741912970652894580730711519000593223296227797745751474334368566144397529399448651289388282095125100324528038524618766793453606448686184876295494992497470077119028509613706947691663467913598771678821928324667620476672366263042188645008200439683148968838329204033918414349024671110025473706249781903199916250828767840318246850682206790661967407614195484523851066057158809365948982796524409393865373207244303311581812471647415989112607739819241372090588686882786055762989845412988100638587430645217573367763548173221202498516941759430505635621314164078584639006176501378371776529294762187249188679903688453083016365983878284537809261262518756324807202428725965732630770841330216003070802945179188330948808319084342394528387479498900792127577904176989915203964127438322224936315734375545242000209372928080399204382873294483023345081480964511288690372334857102976585127543008688976515336566981889241721045468820881460027218480650451896569773528282793034860592525386467529748403531423386956066580591129566946993753707645601423735910946714589803538402484558746554070558676763094531877028300240778867292459085040304288655476846843703109187981993928185085668423072896674459992322992637052029172627979202289144013679031301252748019681055239557525211990089681404194437659210664061136894999476567679799001989042816763792441637296297588721778274069162857242558537181142478277558711658582545276895697386327947796349931953798373870258575566179293017412848518686533831175628991171441532609833548522176082632515615730885996440660222633213525491153993788603133614823603308092263670307429249398052831768852287399239278361307882890742227030045015179537285828942317758313850019192518407369927068430051994277139965802421746868129950797361901106186970024775796489513905851973339847157762501308580800502495027392958090518895906759256028195554314827092856893603657047143804306103220853543636807760756534180130509125170115504065324353561084551767456467878703283665422060927522071396168475416128694559793418710960672785008898349443416966186272115015528492165962940991729769340824231426876504867920577869281501901804096730292773144432424887462051156785427644205604215374952018703981575182328924870014307150085493945632829675123006595247234532574938060508776215235370066650382105593746728547998743762431517604773702760233101859929511114212932267857765990857382140489234741947866140907980598108664549673727187074711239836689116097288620581358830303241790836444847681194821509578811459678263600516453222598318037477754126391457584534319712461178769585092647520675576647939421432808737830198555326796245245489758174268067138918937781344872108036430889485989461562619953240046062044177687824964232124786265135917925812192483511881913668562654848728059461911574833374044736015633178630003140593921205988065743099417245350176222214467669330355585022856544648776913145130334647730048504728338625815682032313221900408277209756778448546602924241895522908887880797012946226052971350804340998708866943504204906305614684021356038664200718847053076037268381198311058380151446417978155424503611683009386886275604564329832152702655546637819729908922776285026346093450116899884844889555780437589419688034337160205185469518791220295215828593362878179851345221062916564888159960917053424992148515196985029835642251456886624559444463830826674111037442858638378057717137174163380674878738179153435460794919216945248979306975608053878633492689395261192727780298007467634434867571622989147503227832641239487734235963289946609903339498202882367309906829047004222354049621383955054611438740970792476532784310988589175419618243361133405450675227693059287434134766374707750287887776110548906026450779914157099487036326203021949261960428516592804550371636947342708587779600097707366437519628712007537425410894371357783438601388840422933314722406392853404054855707157064591548312803154552116411348012701957636877551732560979865303416268276511847018180549254981330913912831070942527131241930418396901280664410091775133475241651254492794081725232927382489444114875946540112363471403147573018808668039222528527061450954391597166486373311930767351781414663084063230624280280559723627734933873050214607251282409184492445126845098928708517988624070907631643228530550999755731583906200928219981156436472764071605541403496527898942666713193984017866489862860732107338521129217992113619708971629968245105907806120668597550336741459329308720382454548626862546672715217922322643682171895173954007746798338974770562166311895871863768014795686917681543776389712810133649719091321492131067452978329901943678682346372614021007083784066720173081620546463342289841923439299298600690930662665317374463481871793977038768887182887252678228705028439822730920891928673622500610671040234497679450047108908818089820986146491258680252643333217015039955333775342848169731653697176955019715950727570925079387235230484698328506124158146351676728199043863628432843633318211955194193390794570262065114980633004152563073594584220260320340579963010782705796140559025717974665875702271696269672331367554175245140803294134068464947482290539833199567295948633841644275395191401751753498272673343336706563841295320515057403077782042781868304428237428900443172697770178315943748473322399413755801374882227727954775447534633771853299368391666957462400111665561642879575670865757057612450710123181072687301531911923788254178734689604634120808179502390340928917890916704470112014516523013574344837212548417489618592316013539449349199148550092473043235509648602435705063335310744320759325819171581114561887147991764664828837631294273650417001081760128415395889311512021495620616254318316641658233590396761698712356492305544893045329238929406427748892068255574554210140628816694001465610496562794430680113061381163415570366751579020832606343999720836095892801060822835607355968873224692047318281746170220190529364553163275988414697979551244024147677705272708238824719963708692466064137906968628956275953519209966151376627002128624768817391911225878493910737341661723139198101685452071047213595282130020588337927905921764315873957497295599678961510276721219946260948459364204208395854416024008095753219108769236137767386676902676483930627769829361063614474648427958264996335973758593013923299717346547091461074083121052447918484140000697909760267997347942910981610077816938269881704295634574449523676588617091810028963255051121889939630805736818229402938200090728268834839655232578427609310116201975084621558432494678438077956520221935303765223156645845692152004745786369822381966011794674948529155180235195589210315106256761000802596224308196950134347628851589489479010363959939979760616952228076909655581533307743308790173430575426597340963813378930104337509160065603517465191750706633632271347314792197368880203789649998255225599330006630142722545974805457654325295739260913563876190808528457270474927591862372195275150922985657954426492654499773179327912900861918553930976724709495062288446103918763303904805108699445161740586942108385385769619988135534075444045084970513312628677112049412011026974212234358097497993509439229507624664130927871026276302474090100150050598457619429807725861046166730641728024566423561433506647590466552674739156227099835991206337020623233415919321631713019506577799490525875004361936001674983424643193635062986355864186760651847716090309522978678856823812681020344069511812122692535855113933768363750567051680217747845203615172558188226262344278884740203091740237987228251387095648532644729036535575950029661164811389887287573716718428307219876469972432564469414104756255016226401926230938339672680322434309243814774749624873503855951425480685347384583173395679938583941096416233381023833618313152109432250410021984157448441916460201695920717451233555501273685312489095159995812541438392015912342534110339533098370380709774226192553302857940468297449139826220469693268660362215165579090623582370799455630386990962068604529434344139302788149492270649405031929371532260878668388177408661060124925847087971525281781065708203929231950308825068918588826464738109362459433995184422654150818299193914226890463063125937816240360121436298286631538542066510800153540147258959416547440415954217119726419373974945039606378895208849495760198206371916111246815786718777262100010468646404019960219143664724151167254074048225564434518616742855148829256377150434448825766828349094462086052273441044073001360924032522594828488676414139651743029626269323376487420176571169347803329029556478347349687685382280071186795547335729490176920124227937327703527933838154726593851415012038943364622954252015214432773842342185155459399099696409254283421153644833722999616149631852601458631398960114457200683951565062637400984052761977876260599504484070209721882960533203056844749973828383989950099452140838189622081864814879436088913703458142862127926859057123913877935582929127263844784869316397389817496597689918693512928778308964650870642425934326691558781449558572076630491677426108804131625780786544299822033011131660676274557699689430156680741180165404613183515371462469902641588442614369961963918065394144537111351502250758976864291447115887915692500959625920368496353421502599713856998290121087343406497539868095055309348501238789824475695292598666992357888125065429040025124751369647904525944795337962801409777715741354642844680182852357190215305161042677181840388037826709006525456258505775203266217678054227588372823393935164183271103046376103569808423770806434727989670935548033639250444917472170848309313605750776424608298147049586488467041211571343825243396028893464075095090204836514638657221621244373102557839271382210280210768747600935199078759116446243500715357504274697281641483756150329762361726628746903025438810761768503332519105279687336427399937188121575880238685138011655092996475555710646613392888299542869107024461737097393307045399029905433227483686359353735561991834455804864431029067941515162089541822242384059741075478940572983913180025822661129915901873887706319572879226715985623058938479254632376033778832396971071640436891509927766339812262274487908713403356945946889067243605401821544474299473078130997662002303102208884391248211606239313256795896290609624175594095683428132742436402973095578741668702236800781658931500157029696060299403287154970862267508811110723383466517779251142827232438845657256516732386502425236416931290784101615661095020413860487838922427330146212094776145444394039850647311302648567540217049935443347175210245315280734201067801933210035942352653801863419059915552919007572320898907771225180584150469344313780228216491607635132777331890986495446138814251317304672505844994242244477789021879470984401716858010259273475939561014760791429668143908992567261053145828244407998045852671249607425759849251491782112572844331227972223191541333705551872142931918902885856858708169033743936908957671773039745960847262448965348780402693931674634469763059636389014900373381721743378581149457375161391632061974386711798164497330495166974910144118365495341452350211117702481069197752730571937048539623826639215549429458770980912168056670272533761384652964371706738318735387514394388805527445301322538995707854974351816310151097463098021425829640227518581847367135429388980004885368321875981435600376871270544718567889171930069442021146665736120319642670202742785357853229577415640157727605820567400635097881843877586628048993265170813413825592350909027462749066545695641553547126356562096520919845064033220504588756673762082562724639704086261646369124472205743797327005618173570157378650940433401961126426353072547719579858324318665596538367589070733154203161531214014027986181386746693652510730362564120459224622256342254946435425899431203545381582161426527549987786579195310046410999057821823638203580277070174826394947133335659699200893324493143036605366926056460899605680985448581498412255295390306033429877516837072966465436019122727431343127333635760896116132184108594758697700387339916948738528108315594793593188400739784345884077188819485640506682485954566074606553372648916495097183934117318630701050354189203336008654081027323167114492096171964964930034546533133265868723174093589698851938444359144362633911435251421991136546044596433681125030533552011724883972502355445440904491049307324562934012632166660850751997766688767142408486582684858847750985797536378546253969361761524234916425306207907317583836409952193181421642181665910597759709669539728513103255749031650207628153679729211013016017028998150539135289807027951285898733293785113584813483616568377708762257040164706703423247374114526991659978364797431692082213769759570087587674913633667166835328192064766025752870153889102139093415221411871445022158634888508915797187423666119970687790068744111386397738772376731688592664968419583347873120005583278082143978783543287852880622535506159053634365076595596189412708936734480231706040408975119517046445894545835223505600725826150678717241860627420874480929615800676972467459957427504623652161775482430121785253166765537216037966290958579055728094357399588233241441881564713682520850054088006420769794465575601074781030812715915832082911679519838084935617824615277244652266461946470321387444603412778727710507031440834700073280524828139721534005653069058170778518337578951041630317199986041804794640053041141780367798443661234602365914087308511009526468227658163799420734898977562201207383885263635411941235998185434623303206895348431447813797675960498307568831350106431238440869595561293924695536867083086156959905084272603552360679764106501029416896395296088215793697874864779983948075513836060997313047422968210210419792720801200404787660955438461806888369333845133824196531388491468053180723732421397913249816798687929650696164985867327354573053704156052622395924207000034895488013399867397145549080503890846913494085214781728722476183829430854590501448162752556094496981540286840911470146910004536413441741982761628921380465505810098754231077921624733921903897826011096765188261157832292284607600237289318491119098300589733747426457759011759779460515755312838050040129811215409847506717381442579474473950518197996998988030847611403845482779076665387165439508671528771329867048190668946505216875458003280175873259587535331681613567365739609868444010189482499912761279966500331507136127298740272882716264786963045678193809540426422863523746379593118609763757546149282897721324632724988658966395645043095927696548836235474753114422305195938165195240255434972258087029347105419269288480999406776703772202254248525665631433855602470600551348710611717904874899675471961475381233206546393551313815123704505007502529922880971490386293052308336532086401228321178071675332379523327633736957811354991799560316851031161670795966081585650975328889974526293750218096800083749171232159681753149317793209338032592385804515476148933942841190634051017203475590606134626792755696688418187528352584010887392260180758627909411313117213944237010154587011899361412569354782426632236451826778797501483058240569494364378685835921415360993823498621628223470705237812750811320096311546916983634016121715462190738737481243675192797571274034267369229158669783996929197054820811669051191680915657605471612520501099207872422095823010084796035872561677775063684265624454757999790627071919600795617126705516976654918519035488711309627665142897023414872456991311023484663433018110758278954531179118539972781519349548103430226471717206965139407474613532470251596468576613043933419408870433053006246292354398576264089053285410196461597515441253445929441323236905468122971699759221132707540914959695711344523153156296890812018006071814914331576927103325540007677007362947970827372020797710855986320968698747251980318944760442474788009910318595805562340789335938863105000523432320200998010957183236207558362703702411278221725930837142757441462818857521722441288341417454723104302613672052203650068046201626129741424433820706982587151481313466168824371008828558467390166451477823917367484384269114003559339777366786474508846006211396866385176396691907736329692570750601947168231147712600760721638692117109257772969954984820462714171057682241686149980807481592630072931569948005722860034197578253131870049202638098893813029975224203510486094148026660152842237498691419199497504972607041909481104093240743971804445685172907143106396342952856195693896779146456363192239243465819869490874829884495934675646438915448232543532121296716334577939072477928603831524583871305440206581289039327214991101650556583033813727884984471507834037059008270230659175768573123495132079422130718498098195903269707226855567575112537948843214572355794395784625047981296018424817671075129985692849914506054367170324876993404752765467425061939491223784764629933349617894406253271452001256237568482395226297239766898140070488885787067732142234009142617859510765258052133859092019401891335450326272812925288760163310883902711379418641169696758209163555152318805178490421188540321736399483546777401681962522245873608542415465680287538821230414907352479324423352060578567191262169801444673203754754510241825731932861081062218655127891963569110514010538437380046759953937955822312175035767875213734864082074187807516488118086331437345151271940538088425166625955263984366821369996859406078794011934256900582754649823777785532330669644414977143455351223086854869665352269951495271661374184317967686778099591722790243221551453397075758104477091112119202987053773947028649195659001291133056495795093694385315978643961335799281152946923962731618801688941619848553582021844575496388316990613113724395435670167847297344453362180270091077223714973653906549883100115155110444219562410580311965662839794814530481208779704784171406637121820148654778937083435111840039082946575007851484803014970164357748543113375440555536169173325888962557141361621942282862825836619325121261820846564539205080783054751020693024391946121366507310604738807272219701992532365565132428377010852496772167358760512265764036710053390096660501797117632690093170952995777645950378616044945388561259029207523467215689011410824580381756638866594549324772306940712565865233625292249712112223889451093973549220085842900512963673796978050738039571483407195449628363052657291412220399902292633562480371287992462574589105628642216561398611159577066685277593607146595945144292842935408451687196845447883588651987298042363122448267439020134696583731723488152981819450745018669086087168929057472868758069581603098719335589908224866524758348745507205918274767072617510555885124053459887636528596852426981191331960777471472938549045608402833513626688069232648218585336915936769375719719440276372265066126949785392748717590815507554873154901071291482011375929092368356771469449000244268416093799071780018843563527235928394458596503472101057333286806015982133510137139267892661478870782007886380291028370031754894092193879331402449663258540670691279617545451373137453327284782077677356317828104826045992253201661025229437833688104128136231985204313082318456223610287189866350280908678507868932547021670098056321317653627385978992916215933279826918379453536657710158076560700701399309069337334682625536518128206022961231112817112747321771294971560177269079108071326377499389328959765502320549952891091181910179013853508741319747356666782984960044666224657151830268346302823044980284049272429074920612764769515301671493875841853648323271800956136371567156366681788044805806609205429737934885019366995847436926405415779739679659420036989217294203859440974282025334124297728303730327668632445824754859196705865931535052517709460166800432704051366158355724604808598248246501727326656663293436158704679484942596922217957218131695571762571099556827302229821684056251526677600586244198625117772272045224552465366228146700631608333042537599888334438357120424329134242942387549289876818927312698468088076211745821265310395365879191820497609659071082109083295529887985483476986425655162787451582510381407683986460550650800851449907526956764490351397564294936664689255679240674180828418885438112852008235335171162368705726349582998918239871584604110688487978504379383745681683358341766409603238301287643507694455106954670761070593572251107931744425445789859371183305998534389503437205569319886938618836584429633248420979167393656000279163904107198939177164392644031126775307952681718253829779809470635446836724011585302020448755975852322294727291761175280036291307533935862093031371043724046480790033848623372997871375231182608088774121506089262658338276860801898314547928952786404717869979411662072094078235684126042502704400321038489723278780053739051540635795791604145583975991904246780891230763862232613323097323516069372230170638936385525351572041735003664026241406986076700282653452908538925916878947552081515859999302090239732002652057089018389922183061730118295704365425550476323411382908189971036744948878110060369194263181770597061799909271731165160344767421572390689883798024915378441567505321561922043479778064696234776843354154307847995254213630177)
∈1⅄2φn25=(1φn26/1φn25)=(1.61803398867044318560479840053315561479506831056314561812729090303232255914695101632789070309896701099633455514828390536487837387537487504165278240586471176274575141619460179940019993335554815061646117960679773408863712095968010663112295901366211262912362545818060646451182939020326557814061979340219926691102965678107297567477507497500833055648117294235254915028323892035988003998667110963012329223592135954681772742419193602132622459180273242252582472509163612129290236587804065311562812395868043985338220593135621459513495501499500166611129623458847050983005664778407197600799733422192602465844718427190936354548483838720426524491836054648450516494501832722425858047317560813062312562479173608797067644118627124291902699100299900033322225924691769410196601132955681439520159946684438520493168943685438187270909696767744085304898367210929690103298900366544485171609463512162612462512495834721759413528823725424858380539820059980006664445184938353882039320226591136287904031989336887704098633788737087637454181939353548817060979673442185938020659780073308897034321892702432522492502499166944351882705764745084971676107964011996001332889036987670776407864045318227257580806397867377540819726757747417527490836387870709763412195934688437187604131956014661779406864378540486504498500499833388870376541152949016994335221592802399200266577807397534155281572809063645451516161279573475508163945351549483505498167277574141952682439186937687437520826391202932355881372875708097300899700099966677774075308230589/1.61803398895790200138026224982746721877156659765355417529330572808833678)
∈1⅄2φn26=(1φn27/1φn26)=(1.6180339887802426828565073768668704126267577207911494072969611097839249380112527081462687304869308773982025322712182745298328569192622309358859242295684265155321970789089980476633743296565699834422083645679734416317250582817790152644715922664404043066733666685887983656388753882019556317085828672163963325727183610257593106686547000238893511157974512533671628512352442068323544191180710584630085754532798431540533638677683227204204525796380351420592620661817402980402494377764780506289489509279777252395113392040727224798793999654016294185002430123647986292455083901048660136910695015363324079642153995699916799156458774393910686777656042770176204558747209476658456418409628232270394503801701910324318535665153674429332828087286746352755101200233950886789188832964009456887958943266909953621708006227706704669956257774336246735808489781124117535607489723460166566441228077401497615183742060909607638002191230136828317942550229420147784468626691819132898931569365614162266358027233860272009094428838565650408178395788884037794601006647829776016739021195620834809255887901279315940787360061947558755447183939765884359065184977717001804057894606773042926692642903627062515960557857537090277034095870437339879564719547255607819231751418945079205555509790515103836300280905818292652788875800087319697181880339064031698697618478824973433394017776972313065827518884943942401950689084214081536826670401093967526957897078085227319532427734712874712709958564332375013386274332127882167835048149399059253828474458988574300000823770728130946594943695270732249800235598428245450726153896847429423442867381150478198907680014498364815104660071009036764887596484146532337119932780308584514757852594465908248416300775168255171220745842017249759047062021698120978969133310816933431087459738205662599985172126893642961291013485126819503595759228291581886929229856746270378028387139291392419661759739029433328116118721837338232023263285362417931841209954445478734358653299613651528506586046971406918026574843689504337152883609433822378555600405295198240425724712298073200266901715914426696761757267717248935276333890751526035273862578567133195489031492754936446088324697470200093909863006927911823581260863476477226858220819981382781544240606954272486881451154514675475521652813588921931248095030191197185999192704686431672336955178634682395195769113540319458288369181089519165025989966472531365070473585791602481197433130411143970410155445536398309622465875297587175537304457423409916552025240335109932203669074823095236133879218735841440610249355399405237534289456558450652014531315644229897934806784575716886476155956274249750809354740388655029532180603494435428731475455751155338446203652599408532617201980344830426795614244643430840328519766378621502063545673968021220333956653184285749590174062754854069015511602810705724382789781947888263738436318403861837173477877637096043429192787063504485431614673004209468420749137100162282833441796479203907968334253210646412890364353793052317678943596418244874086644205184812962856177868575/1.61803398867044318560479840053315561479506831056314561812729090303232255914695101632789070309896701099633455514828390536487837387537487504165278240586471176274575141619460179940019993335554815061646117960679773408863712095968010663112295901366211262912362545818060646451182939020326557814061979340219926691102965678107297567477507497500833055648117294235254915028323892035988003998667110963012329223592135954681772742419193602132622459180273242252582472509163612129290236587804065311562812395868043985338220593135621459513495501499500166611129623458847050983005664778407197600799733422192602465844718427190936354548483838720426524491836054648450516494501832722425858047317560813062312562479173608797067644118627124291902699100299900033322225924691769410196601132955681439520159946684438520493168943685438187270909696767744085304898367210929690103298900366544485171609463512162612462512495834721759413528823725424858380539820059980006664445184938353882039320226591136287904031989336887704098633788737087637454181939353548817060979673442185938020659780073308897034321892702432522492502499166944351882705764745084971676107964011996001332889036987670776407864045318227257580806397867377540819726757747417527490836387870709763412195934688437187604131956014661779406864378540486504498500499833388870376541152949016994335221592802399200266577807397534155281572809063645451516161279573475508163945351549483505498167277574141952682439186937687437520826391202932355881372875708097300899700099966677774075308230589)
∈1⅄2φn27=(1φn28/1φn27)=(1.6180339887383030068527324379639340589966296367949984217332423708621409443126393711370648311254569336822490810414524127116659369304238919040006516714354081601482552515553564337280697288435886731358633119164231384089034609862639880255373743750572758097526703255302467187324990581311285116435357248317363989043773992200307507458583225569957946827683817165432903298068405135985500310562168436701320652893319349550448533230152022727041309859585170401897993055626266431793420154975613233003085256952010508201895956582390615931330122493865124377602867354315795904652323106843568308403506806911790161797798572432261808999175228339561547312364447250252013562911749432333085562422995855776965451231557189259640155179260556568135303281776619250781496604180879552790477451150098259833620136647354112148581087273060513802197354621266889999898176338217474976835116944475557229989104868189269822521357513058884623608834220896251871009785253897300654726145261635898950198047022167011170055697542995041187671191031371870195195959637100469407080817440356790110885967681169750226557647466118176541864798541885163274241668278874644889979533443981712470343858505839587003227810078506043234326792860124835809345375678400146626072966836033357431599955197588815688989807451455569245181195206142003278721909397305745909234387887057194350823244305511714812288079503915119795538087140689753484914824506918917818122575324053803622885886222240324206539115559673756987648789825779714690099685364885091997678420511358429471840666334042704843751590994715351953486951297742569418281420236434542659023103788858454927756111965298496064515472105407854677269903980286939078903155515278640450467879725890702481442637640134814528200063130670305165514362227494425154517406754981722652710036758341903491533362522783044323839973933142583673594069789937785742650877210846256453074565467523343074463643861560549440478978505024997708967609893186978790131250700037674754859534258571006730544043824904031198769970165667097720168212689264731338268386807726379456057998757751326253194717388426722601798205867079391909091834760561659318392408027777494934272826319380097547067987658972191957967192416173670437536274679510024539502489588530582736816381390707572625726766385972772352839352808805710270952764003299086641753810750542210998991945748353002270667657750308016576892138195073771242961439379282957773727458786872893522996874013583276481788838090195399606960665519453410583551405675650907757944791210581514932440000407294647130100092659532222097771080043580527242920709914569947764461505564663116414992515960858984410797381095418953456404199207811911331955319777209828019835249315235874512519219216161451598122371676730238572839556456129275320999093769410135527293832540805832459346903033326884501420440081866224073150118624565976641651987088759685975827062692828559500656762618497286399413495708132655866570273600179209644737244040770194177723019275219175431986885112362410777016363062448451771222596707022777953140750847681984339520817847651437240986060340701972324328727509698703784785508456455111038703173843537761304972049404840696881141239601258540459632009286317954566282112637334663829180624993636021138592186052194809029722326874319054261829363907584844566180288975552138806015741938111578368581290920384078852243684387377938885438198128481096437190074229449439460741887199747477318779337942551090022299381930372980073109389159852966632386033866549908867822704640104267429665305623720840248857029396491156614974187701738129906627702145424553757802238084085979900009164129560427252084839474997199849300980561862965715973077823824700383875204920119337331609119327149242941074646926452769094482175768004968994694987221130446293109592807176531682432363632660957753362726430367888890020262908694722479609811728049364111232168131230335305318249854901281959901841990041645877669052734474437169709497092934456108910588642588764777158916188943986803653432984756997831156004032217006587990917329368998767933692431447219704915028154242482868168905090164852508425908012503945666894072844647639218401572157337922186357665794377297396368968220835157673940270239998370821411479599629361871111608915679825677891028317160341720208942153977741347534340029936156564062356810475618324186174383203168752354672178720891160687920659002739056501949923123135354193607510513293079045708641774175482898716003624922359457890824669836776670162612387866692461994318239672535103707399525501736093433392051644961256096691749228685761997372949526010854402346017167469376533718905599283161421051023836919223289107922899123298272052459550550356891934547750206192915109613171908888187436996609272062641916728609394251036055758637192110702685089961205184860857966174179555845187304625848954780111802380637212475435041594965838161471962854728181734871549450661344683277500025455915445631255791220763881110692502723782952682544369660621735278844097791444775937032247553686525674836318463684591025262450488244458247207486075614251239703082202242157032451201010090724882648229795639910802472278508079707562443360588133470455864533800364528709181439582930281338777505116639004571882414035373540103249193047480373489191418301784968791047663656080399963343481758290991660642100011200602796077752548137136107688704701198464499180319522650673563522691403028235701412294188923622071296927980124021220051115478214827561628771293873270270545469356168986549094278528444439918948365221110081560753087802543555071327475078658778727000580394872160392632039833416489323789062102251321162011628262175564357645429644940891364335244224052785386268060972008675375983871131973648036330682524004928265230274211121/1.6180339887802426828565073768668704126267577207911494072969611097839249380112527081462687304869308773982025322712182745298328569192622309358859242295684265155321970789089980476633743296565699834422083645679734416317250582817790152644715922664404043066733666685887983656388753882019556317085828672163963325727183610257593106686547000238893511157974512533671628512352442068323544191180710584630085754532798431540533638677683227204204525796380351420592620661817402980402494377764780506289489509279777252395113392040727224798793999654016294185002430123647986292455083901048660136910695015363324079642153995699916799156458774393910686777656042770176204558747209476658456418409628232270394503801701910324318535665153674429332828087286746352755101200233950886789188832964009456887958943266909953621708006227706704669956257774336246735808489781124117535607489723460166566441228077401497615183742060909607638002191230136828317942550229420147784468626691819132898931569365614162266358027233860272009094428838565650408178395788884037794601006647829776016739021195620834809255887901279315940787360061947558755447183939765884359065184977717001804057894606773042926692642903627062515960557857537090277034095870437339879564719547255607819231751418945079205555509790515103836300280905818292652788875800087319697181880339064031698697618478824973433394017776972313065827518884943942401950689084214081536826670401093967526957897078085227319532427734712874712709958564332375013386274332127882167835048149399059253828474458988574300000823770728130946594943695270732249800235598428245450726153896847429423442867381150478198907680014498364815104660071009036764887596484146532337119932780308584514757852594465908248416300775168255171220745842017249759047062021698120978969133310816933431087459738205662599985172126893642961291013485126819503595759228291581886929229856746270378028387139291392419661759739029433328116118721837338232023263285362417931841209954445478734358653299613651528506586046971406918026574843689504337152883609433822378555600405295198240425724712298073200266901715914426696761757267717248935276333890751526035273862578567133195489031492754936446088324697470200093909863006927911823581260863476477226858220819981382781544240606954272486881451154514675475521652813588921931248095030191197185999192704686431672336955178634682395195769113540319458288369181089519165025989966472531365070473585791602481197433130411143970410155445536398309622465875297587175537304457423409916552025240335109932203669074823095236133879218735841440610249355399405237534289456558450652014531315644229897934806784575716886476155956274249750809354740388655029532180603494435428731475455751155338446203652599408532617201980344830426795614244643430840328519766378621502063545673968021220333956653184285749590174062754854069015511602810705724382789781947888263738436318403861837173477877637096043429192787063504485431614673004209468420749137100162282833441796479203907968334253210646412890364353793052317678943596418244874086644205184812962856177868575)
∈1⅄2φn28=(1φn29/1φn28)=(1.618033988754322537608830405492572629644663022991652271318488032195235533068395996362/1.6180339887383030068527324379639340589966296367949984217332423708621409443126393711370648311254569336822490810414524127116659369304238919040006516714354081601482552515553564337280697288435886731358633119164231384089034609862639880255373743750572758097526703255302467187324990581311285116435357248317363989043773992200307507458583225569957946827683817165432903298068405135985500310562168436701320652893319349550448533230152022727041309859585170401897993055626266431793420154975613233003085256952010508201895956582390615931330122493865124377602867354315795904652323106843568308403506806911790161797798572432261808999175228339561547312364447250252013562911749432333085562422995855776965451231557189259640155179260556568135303281776619250781496604180879552790477451150098259833620136647354112148581087273060513802197354621266889999898176338217474976835116944475557229989104868189269822521357513058884623608834220896251871009785253897300654726145261635898950198047022167011170055697542995041187671191031371870195195959637100469407080817440356790110885967681169750226557647466118176541864798541885163274241668278874644889979533443981712470343858505839587003227810078506043234326792860124835809345375678400146626072966836033357431599955197588815688989807451455569245181195206142003278721909397305745909234387887057194350823244305511714812288079503915119795538087140689753484914824506918917818122575324053803622885886222240324206539115559673756987648789825779714690099685364885091997678420511358429471840666334042704843751590994715351953486951297742569418281420236434542659023103788858454927756111965298496064515472105407854677269903980286939078903155515278640450467879725890702481442637640134814528200063130670305165514362227494425154517406754981722652710036758341903491533362522783044323839973933142583673594069789937785742650877210846256453074565467523343074463643861560549440478978505024997708967609893186978790131250700037674754859534258571006730544043824904031198769970165667097720168212689264731338268386807726379456057998757751326253194717388426722601798205867079391909091834760561659318392408027777494934272826319380097547067987658972191957967192416173670437536274679510024539502489588530582736816381390707572625726766385972772352839352808805710270952764003299086641753810750542210998991945748353002270667657750308016576892138195073771242961439379282957773727458786872893522996874013583276481788838090195399606960665519453410583551405675650907757944791210581514932440000407294647130100092659532222097771080043580527242920709914569947764461505564663116414992515960858984410797381095418953456404199207811911331955319777209828019835249315235874512519219216161451598122371676730238572839556456129275320999093769410135527293832540805832459346903033326884501420440081866224073150118624565976641651987088759685975827062692828559500656762618497286399413495708132655866570273600179209644737244040770194177723019275219175431986885112362410777016363062448451771222596707022777953140750847681984339520817847651437240986060340701972324328727509698703784785508456455111038703173843537761304972049404840696881141239601258540459632009286317954566282112637334663829180624993636021138592186052194809029722326874319054261829363907584844566180288975552138806015741938111578368581290920384078852243684387377938885438198128481096437190074229449439460741887199747477318779337942551090022299381930372980073109389159852966632386033866549908867822704640104267429665305623720840248857029396491156614974187701738129906627702145424553757802238084085979900009164129560427252084839474997199849300980561862965715973077823824700383875204920119337331609119327149242941074646926452769094482175768004968994694987221130446293109592807176531682432363632660957753362726430367888890020262908694722479609811728049364111232168131230335305318249854901281959901841990041645877669052734474437169709497092934456108910588642588764777158916188943986803653432984756997831156004032217006587990917329368998767933692431447219704915028154242482868168905090164852508425908012503945666894072844647639218401572157337922186357665794377297396368968220835157673940270239998370821411479599629361871111608915679825677891028317160341720208942153977741347534340029936156564062356810475618324186174383203168752354672178720891160687920659002739056501949923123135354193607510513293079045708641774175482898716003624922359457890824669836776670162612387866692461994318239672535103707399525501736093433392051644961256096691749228685761997372949526010854402346017167469376533718905599283161421051023836919223289107922899123298272052459550550356891934547750206192915109613171908888187436996609272062641916728609394251036055758637192110702685089961205184860857966174179555845187304625848954780111802380637212475435041594965838161471962854728181734871549450661344683277500025455915445631255791220763881110692502723782952682544369660621735278844097791444775937032247553686525674836318463684591025262450488244458247207486075614251239703082202242157032451201010090724882648229795639910802472278508079707562443360588133470455864533800364528709181439582930281338777505116639004571882414035373540103249193047480373489191418301784968791047663656080399963343481758290991660642100011200602796077752548137136107688704701198464499180319522650673563522691403028235701412294188923622071296927980124021220051115478214827561628771293873270270545469356168986549094278528444439918948365221110081560753087802543555071327475078658778727000580394872160392632039833416489323789062102251321162011628262175564357645429644940891364335244224052785386268060972008675375983871131973648036330682524004928265230274211121)
while alternately set path variable ∈2⅄2φn28=(1φn28/1φn29) and set path ∈3⅄2φn29=(1φn29cn/1φn29cn)
Moving forward to ∈1⅄3φn
4th tier 3rd divide 1⅄3φn
1⅄3φn1=(1⅄2φn2/1⅄2φn1)=2/0=0
1⅄3φn2=(1⅄2φn3/1⅄2φn2)=0.75/2=0.375
next set of decimal shift group array
1⅄3φn3=(2φn4c1/2φn3)=1.106/0.75=1.608
next set of decimal shift group array
1⅄3φn4=(1⅄2φn5c1/1⅄2φn4c1)(0.963855421686746987951807228915662650602409/1.06)=0.9092975676290065924073653102977949533984990566037735849056603773
1⅄3φn5=(1⅄2φn6c1/1⅄2φn5c1)=(1.015625/0.963855421686746987951807228915662650602409)=1.0537109375000000000000000000000000000000006980834960937500000000000000000000000000004624803161621093750000000000000000000000003063932094573974609375000000000000000000002029855012655258178710937500000000000000001344778945884108543395996093750000000000000890916051648221909999847412109375000000000590231884216947015374898910522460937500000391028623293727397685870528221130371093750259056462932094400966889224946498870849609546624906692512540640564111527055501937866324639000 extended shell factoring to divisor 963,855,421,686,746,987,951,807,228,915,662,650,602,409 potential digits long and less
1⅄3φn6=(1⅄2φn7c1/1⅄2φn6c1)=(0.9940824061538/1.015625)=0.97878883067451076923
1⅄3φn7=(1⅄2φn8c1/1⅄2φn7c1)=[(1φn9c1/1φn8c1)/(1φn8c1/1φn7)]=[(1.619047 /1.615384)/(1.615384/1.625)]
1⅄3φn8=(1⅄2φn9c1/1⅄2φn8c1)=[(1φn10c1/1φn9c1)/(1φn9c1/1φn8)]=[(1.61762941/1.619047619047)/(1.619047 /1.615384)]
1⅄3φn9=(1⅄2φn10c1/1⅄2φn9c1)=[(1φn11c1/1φn10c1)/(1φn10c1/1φn9)]=[(1.618/1.61762941)/(1.61762941/1.619047619047)]
1⅄3φn10=(1⅄2φn11c1/1⅄2φn10c1)=[(1φn12c1/1φn11c1)/(1φn11c1/1φn10)]=[(1.61797752808988764044943820224719101123595505/1.618)/(1.618/1.61762941)]
and so on for variables of ∈1⅄3φn
Variables 1⅄3φn shown are based on one cycle in decimal stem of variable variant change potential of factors based in 1φnc1 from 1⅄(Yn2/Yn1) path function of Y base.
Examples of alternate path with variables of ∈⅄3φ variables (1⅄2φn/1⅄2φn)
2⅄3φn1 example of 2⅄3φn1=(1⅄2φn1/1⅄2φn2)=(0/2)=0
3⅄3φn4 example of 3⅄3φn4(1⅄2φn4c1/1⅄2φn4c2)=(1.106/1.1066) and 3⅄3φn4(1⅄2φn4c2/1⅄2φn4c1)=(1.1066/1.106) for ∈3⅄3φn4 of cn
Examples of alternate path functions with variables of ∈⅄3φ variables (1⅄2φn/1⅄2φn)
⅄ncn=(⅄n)(ncn) example
⅄ncn=(1⅄3φn4)(2)=(0.9092975676290065924073653102977949533984990566037735849056603773)(0.909297567629006592407365310297794953398499056603773^5849056603773)
X⅄=(n2xn1) example
X3φn3=(2φn4c1x2φn3)=1.106x0.75=0.8295
+⅄=(nncn+nncn) example
X3φn3=(2φn4c1+2φn3)=1.106+0.75=1.856
1-⅄=(n2-n1) example
1-⅄3φn3=(2φn4c1-2φn3)=1.106-0.75=0.356
2-⅄=(n1-n2) example
2-⅄3φn3=(2φn3-2φn4c1)=0.75-1.106= - 0.356
Moving forward to ∈1⅄4φn
5th tier 4th divide 1⅄4φn
1⅄4φn1=(1⅄3φn2/1⅄3φn1)=0.375/0=0
1⅄4φn2=(1⅄3φn3c1/1⅄3φn2)=1.608/0.375=4.023703
next set not included in previous set shift has variable of potential change dependent of root base decimal shell numerals
1⅄4φn3=(1⅄3φn4c1/1⅄3φn3c1)=(0.9092975676290065924073653102977949533984990566037735849056603773/1.608)=0.5654835619583374330891575312797232297254347366938890453393410306592039800995024875621890547263681592039800995024875621890547263681592039800995024875621890547263681
1⅄4φn4=(1⅄3φn5c1/1⅄3φn4c1)=[(1.015625/0.963855421686746987951807228915662650602409)/(0.963855421686746987951807228915662650602409/1.06)]
and so on for variables of ∈1⅄4φn
6th tier 5th divide 1⅄5φn
1⅄5φn1=(1⅄4φn2/1⅄4φn1)=4.023703/0=0
next set not included in previous set shift has variable of potential change dependent of root base decimal shell numerals
1⅄5φn2=(1⅄4φn3/1⅄4φn2)=(0.5654835619583374330891575312797232297254347366938890453393410306592039800995024875621890547263681592039800995024875621890547263681592039800995024875621890547263681/4.023703)
1⅄5φn3=(1⅄4φn4/1⅄4φn3)=[(1⅄3φn5c1/1⅄3φn4c1)/(1⅄3φn4c1/1⅄3φn3c1)]
and so on for variables of ∈1⅄5φn
7th tier 6th divide 6φn
1⅄6φn1=(1⅄5φn2c1/1⅄5φn1c1)=[(1⅄4φn3/1⅄4φn2)/(1⅄4φn2/1⅄4φn1)]=0
1⅄6φn2=(1⅄5φn3c1/1⅄5φn2c1)=[(1⅄4φn4c1/1⅄4φn3c1)/(1⅄4φn3c1/1⅄4φn2c1)]
1⅄6φn4=(1⅄5φn4c1/1⅄5φn3c1) and so on for variables of ∈1⅄6φn
Alternate Path of φn 3rd tier 2nd divide 2⅄2φn from Y base numeral ratios 1φn
Previous φ divided by later φ of ordinal ratios from Y base
∈2⅄2φn1=(1φn1/1φn2)=(0/1)=0
∈2⅄2φn2=(1φn2/1φn3)=(1/2)=0.5
∈2⅄2φn3=(1φn3/1φn4)=(2/1.5)=1.3 and ∈2⅄2φn3=(1φn3/1φn4)c2=1.33 and ∈2⅄2φn3=(1φn3/1φn4)c3=1.333 and so on for cn
∈2⅄2φn4=(1φn4/1φn5)=(1.5/1.^6)=0.9375 and 2⅄2φn4=(1φn4/1φn5c2)=(1.5/1.66)=0.90361445783132530120481927710843373493875 and so on for cn
∈2⅄2φn5=(1φn5/1φn6)=(1.^6/1.6)=1 and 2⅄2φn5=(1φn5c2/1φn6)=(1.66/1.6)=1.0375 and so on . . . for variable ∈2⅄2φn5cn
∈2⅄2φn6=(1φn6/1φn7)=(1.6/1.625)=0.98406153 2⅄2φn6c2=0.984061538406153 2⅄2φn6c3=0.9840615384061538406153 and so on . . . to cn
∈2⅄2φn7=(1φn7/1φn8)=(1.625/1.615384)=1.005952764172481589516796006398478627991858282612679090544415445491 extended shell (966456/1615384) and 2⅄2φn7=(1φn7/1φn8c2)=(1.625/1.615384615384) and so on . . . for cn ∈2⅄c1 ∈2⅄c2 ∈2⅄cn
∈2⅄2φn8=(1φn8/1φn9)=(1.615384/1.619047) and 2⅄2φn8=(1φn8c2/1φn9c2)=(1.615384615384/1.619047619047) and so on . . . for cn ∈2⅄c1 ∈2⅄c2 and cn ∈2⅄c2 to of ∈2⅄c1 (1φn8/1φn9) and more for those of ∈2⅄c3 to ∈2⅄cn
∈2⅄2φn9=(1φn9/1φn10)=(1.619047/1.61762941) and 2⅄2φn9=(1φn9c2/1φn10c2)=(1.619047619047/1.617629411762941) and so on for cn
∈2⅄2φn10=(1φn10/1φn11)=(1.61762941/1.618) and so on for cn
∈2⅄2φn11=(1φn11/1φn12)=(1.618/1.61797752808988764044943820224719101123595505) and so on for cn
∈2⅄2φn12=(1φn12/1φn13)=(1.61797752808988764044943820224719101123595505/1.61805) and so on for cn
∈2⅄2φn13=(1φn13/1φn14)=(1.61805/1.61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832) and so on for cn
∈2⅄2φn14=(1φn14/1φn15)=(1.61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832/1.61830223896551724135014) and so on for cn
∈2⅄2φn15=(1φn15/1φn16)=(1.61830223896551724135014/1.618032786885245901639344262295081967213114754098360655737704918) and so on for cn
∈2⅄2φn16=(1φn16/1φn17)=(1.618032786885245901639344262295081967213114754098360655737704918/1.6180344478216818642350572441742654508601925025329280648429584599797365754812563323201418439716312056737588652482269503546099290780141843) and so on for cn
∈2⅄2φn17=(1φn17/1φn18)=(1.6180344478216818642350572441742654508601925025329280648429584599797365754812563323201418439716312056737588652482269503546099290780141843/1.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129) and so on for cn
∈2⅄2φn18=(1φn18/1φn19)=(1.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/1.618034055731424148606811145510835913312693) and so on for cn
∈2⅄2φn19=(1φn19/1φn20)=(1.618034055731424148606811145510835913312693/1.61803396316670629036115761779478593637885673283903372398947620186558239655584788327911265247548433389141353743123654628079406840468787371442238722793590050227218368811289165271466156421908634298014828988280315713944032525711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242) and so on for cn
∈2⅄2φn20=(1φn20/1φn21)=(1.61803396316670629036115761779478593637885673283903372398947620186558239655584788327911265247548433389141353743123654628079406840468787371442238722793590050227218368811289165271466156421908634298014828988280315713944032525711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242/1.61803399852) and so on for cn
∈2⅄2φn21=(1φn21/1φn22)=(1.61803399852/1.6180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981) and ∈2⅄2φn21=(1φn21c2/1φn22) and ∈2⅄2φn21=(1φn21/1φn22c2) and ∈2⅄2φn21=(1φn21c2/1φn22c2)=(1.61803399852/1.6180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981) and so on for cn
∈2⅄2φn22=(1φn22/1φn23)=(1.6180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981/1.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793292304217717802495624188357517983174298458585060132121280560103890237705381401388967308452374230704082208796792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869) and ∈2⅄2φn22=(1φn22c2/1φn23) and ∈2⅄2φn22=(1φn22/1φn23c2) and
∈2⅄2φn22=(1φn22c2/1φn23c2)=(1.6180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981/1.61803399017559708655637739258088193777878154819039015301225227259894980520580430241093105979329230421771780249562418835751798317429845858506013212128056010389023770538140138896730845237423070408220879679295353170346112585398904635537236745525379707526396025069166054994071481000508158771385014962452713003218338885438428095533849020382812941110044605047710462424481960363615831963186720117441138275647902433515894077127209079103382078933995821805657500988086499915306871322906668172322285585229518378408898424707808706453616396589690023149455140872903845068036813279882558861724515272994184405171927050985263395629834566032409237197222065383098789452882389475467223759245666534921800011292417141889221387838066738185308565298402122974422675173620913556546778838010276099599119191462932640721748630794421545931906724634407995031336457568742589351250635198464231268703068891254022923606798035119417311275478516176387555756309638078030602450454519789961041160860482186211958669753260685449720512675738241770651007848229913613009429143470159787702557732482637908644345322116198972390040088080853706735926825136920557845406809327536559200496866354243125741064874936480153576873129693410874597707639320196488058268872452148382361244424369036192196939754952854158432612500705776071368076336739879171136581785331150132685901417198351307097284173677375564225622494494946643329004573428942465134662074417028965049968945852859804641183445316469990401445429394161820337643272542487719496358195471740726102422223476935237587691265315340748687256507255378013663937665857376771497939133871605217096719552820281181186833041613557167861780814183275930212862063124611823160747558014793066455874880016938625715656536310767319744791372593303596634759691717012026424256112020778047541076167353622042798260967760149059906272937722319762480944046073061938908023262379312291798058946417480661735644514708373327310710857659081926486364406301168765174179888205070295296708260403139291965445203545818982553215515781152956354807746598159336005872056913782395121675794703856360453955169103946699791090282875049404324995765343531791541979560724973180509288013099203884478572638473265202416577268364293376997346281971599570888148608209587262153463978958274518660719326971373722545310823781830500818700242786996792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869) and so on for cn
So now functions between ∈1⅄2φn and ∈2⅄2φn variables are applicable to set function paths 1⅄, 2⅄, 1X, 1+⅄, 1-⅄, 2-⅄, 3⅄nc ⅄n, ⅄ncn written as examples
1⅄(∈1⅄2φn2/∈2⅄2φn1)=(2/0)
1⅄(∈2⅄2φn2/∈1⅄2φn1)=(0.5/0)
and
2⅄(∈1⅄2φn1/∈2⅄2φn2)=(0/0.5)
2⅄(∈2⅄2φn1/∈1⅄2φn2)=(0/2)
and
3⅄(∈1⅄2φn3/∈2⅄2φn3c1)=(0.75/1.3) or 3⅄(∈1⅄2φn3c2/∈2⅄2φn3cn)=(0.75/1.33) for cn variant path
3⅄(∈2⅄2φn3c1/∈1⅄2φn3)=(1.3/0.75) or 3⅄(∈2⅄2φn3c2/∈1⅄2φn3)=(1.33/0.75) for cn variant path
Then for sets of 1⅄3φ of (∈2⅄2φn2/∈2⅄2φn1) variables path base sets for cn factoring before variable change in stem decimal cycle are
1⅄3φn1 of (∈2⅄2φn2/∈2⅄2φn1)=(0.5/0)=0
1⅄3φn2 of (∈2⅄2φn3/∈2⅄2φn2)=(1.3/0.5)=2.6 and 1⅄3φn2 of (∈2⅄2φn3c2/∈2⅄2φn2)=(1.33/0.5)=2.66
Now in this set a cn variable change of previous tier and current tier decimal stem cycle multiple path potentials quantify varying quotients similar to the detail in tRNA genome prediction from variable 0.721153846 while yet variable 0.69508804448563484708063021316033364226057692307 in web searches displayed zero web results and 0.70488721804511278195 in web search results displays one result of an xml for treasury program shell framework to extended firewall encryption defense potential and factorable divisors using common universal numbers.
1⅄3φn3 of (∈2⅄2φn4/∈2⅄2φn3)=((1φn4/1φn5)/(1φn3/1φn4))=(1.5/1.6)/(2/1.5)=(0.9375/1.3)=0.721153846
and
1⅄3φn3 of (∈2⅄2φn4/∈2⅄2φn3)=((1φn4/1φn5c2)/(1φn3/1φn4))=(1.5/1.66)/(2/1.5)=(0.90361445783132530120481927710843373493875/1.3)=0.69508804448563484708063021316033364226057692307
while
1⅄3φn3 of (∈2⅄2φn4/∈2⅄2φn3c2)=((1φn4/1φn5)/(1φn3/1φn4))=(1.5/1.6)/(2/1.5)=(0.9375/1.33)=0.70488721804511278195
1⅄3φn4 of (∈2⅄2φn5/∈2⅄2φn4)
1⅄3φn5 of (∈2⅄2φn6/∈2⅄2φn5)
1⅄3φn6 of (∈2⅄2φn7/∈2⅄2φn6)
1⅄3φn7 of (∈2⅄2φn8/∈2⅄2φn7)
1⅄3φn8 of (∈2⅄2φn9/∈2⅄2φn8)
1⅄3φn9 of (∈2⅄2φn10/∈2⅄2φn9)
1⅄3φn10 of (∈2⅄2φn11/∈2⅄2φn10)
and so on for variables of set ∈1⅄3φn of (∈2⅄2φn/∈2⅄2φn)
Alternate Path of φn 4th tier 3rd divide sets 1⅄2φn and 2⅄2φn from Y base numerals examples
1⅄3φn=(1⅄2φn2/1⅄1φn1)
2⅄3φn=(1⅄2φn1/1⅄1φn2) each with alternate stem cycle variant paths determined of cn
Examples of 1⅄3φn=(1⅄2φn2/1⅄1φn1) and quotients below
1⅄3φn1=(1⅄2φn2/1⅄2φn1)=(0.5/0)=0
1⅄3φn2=(1⅄2φn3/1⅄2φn2)=(1.3/0.5)=2.6 and 1⅄3φn=(1⅄2φn3c2/1⅄2φn2)=(1.33/0.5)=2.66 and so on for cn . . .
(1⅄3φn3)c1=∈(1⅄2φn4/1⅄2φn3c1)=(0.9375/1.3)=0.721153846 and
(1⅄3φn3)c2=∈(1⅄2φn4/1⅄2φn3c2)=(0.9375/1.33)=0.70488721804511278195
while
∈(1⅄3φn3)c2 of 1φn5c2=(2⅄2φn4=(1φn5c2/1φn4)/1⅄2φn3c1)=(0.90361445783132530120481927710843373493875/1.3)=0.61816496765625576163113994439295644114913461538
while
∈(1⅄3φn3)c2 of 1⅄2φn3c2 and 1φn5c2=(2⅄2φn4=(1φn5c2/1φn4)/1⅄2φn3c2)=(0.90361445783132530120481927710843373493875/1.33)=0.679409366790470151281819005344687018750939849624060150375
Examples of 2⅄3φn=(1⅄2φn1/1⅄1φn2) and quotients below
2⅄3φn1=(1⅄2φn1/1⅄2φn2)=(0/0.5)=0
2⅄3φn2=(1⅄2φn2/1⅄2φn3c1)=(0.5/1.3)=0.384615 and 2⅄3φn2=(1⅄2φn2/1⅄2φn3c2)=(0.5/1.33)=0.37593984962406015
(2⅄3φn3)c1=∈(1⅄2φn3c1/1⅄2φn4)=(1.3/0.9375) and (2⅄3φn3)c2=∈(1⅄2φn3c2/1⅄2φn4)=(1.33/0.9375)
while
(2⅄3φn3)c2 of 1φn5c2=(1⅄2φn3c1/(1φn5c2/1φn4))=(1.3/0.90361445783132530120481927710843373493875)
while
∈(2⅄3φn3)c2 of 1⅄2φn3c2 and 1φn5c2=(1⅄2φn3c2/(2⅄2φn4=(1φn5c2/1φn4))=(1.33/0.90361445783132530120481927710843373493875)
Base sets of φn 5th tier 4th divide sets of 1⅄3φn and 2⅄3φn and 3⅄3φn from Y base
∈3⅄4φn : (1⅄3φn1cn)/(1⅄3φn1cn) ∈3⅄4φn : (2⅄3φn1cn)/(2⅄3φn1cn) ∈3⅄4φn : (3⅄3φn1cn)/(3⅄3φn1cn)
∈3⅄4φn : (1⅄3φn1cn)/(1⅄2φn1cn) ∈3⅄4φn : (2⅄3φn1cn)/(2⅄2φn1cn) ∈3⅄4φn : (3⅄3φn1cn)/(3⅄2φn1cn)
∈3⅄4φn : (1⅄3φn1cn)/(1⅄1φn1cn) ∈3⅄4φn : (2⅄1φn1cn)/(2⅄2φn1cn) ∈3⅄4φn : (3⅄3φn1cn)/(3⅄1φn1cn)
∈2⅄4φn : (1⅄3φn1cn)/(1⅄3φn2cn) ∈2⅄4φn : (2⅄3φn1cn)/(2⅄3φn2cn) ∈2⅄4φn : (3⅄3φn1cn)/(3⅄3φn2cn)
∈2⅄4φn : (1⅄3φn1cn)/(1⅄2φn2cn) ∈2⅄4φn : (2⅄3φn1cn)/(2⅄2φn2cn) ∈2⅄4φn : (3⅄3φn1cn)/(3⅄2φn2cn)
∈2⅄4φn : (1⅄3φn1cn)/(1⅄1φn2cn) ∈2⅄4φn : (2⅄1φn1cn)/(2⅄2φn2cn) ∈2⅄4φn : (3⅄3φn1cn)/(3⅄1φn2cn)
∈1⅄4φn : (1⅄3φn2cn)/(1⅄3φn1cn) ∈1⅄4φn : (2⅄3φn2cn)/(2⅄3φn1cn) ∈1⅄4φn : (3⅄3φn2cn)/(3⅄3φn1cn)
∈1⅄4φn : (1⅄3φn2cn)/(1⅄2φn1cn) ∈1⅄4φn : (2⅄3φn2cn)/(2⅄2φn1cn) ∈1⅄4φn : (3⅄3φn2cn)/(3⅄2φn1cn)
∈1⅄4φn : (1⅄3φn2cn)/(1⅄1φn1cn) ∈1⅄4φn : (2⅄1φn2cn)/(2⅄2φn1cn) ∈1⅄4φn : (3⅄3φn2cn)/(3⅄1φn1cn)
Examples all equal zero where any nφn1=0 and are a base 0 of the tier set scale defined in each of the array.
∈1⅄4φn2cn →∈1⅄4φncn bases vary to the cycle stem of the defined cn in the variable variants applicable to P,Q,P/Q,Q/P
∈2⅄4φn2cn →∈2⅄4φncn bases vary to the cycle stem of the defined cn in the variable variants applicable to P,Q,P/Q,Q/P
∈3⅄4φn2cn →∈3⅄4φncn bases vary to the cycle stem of the defined cn in the variable variants applicable to P,Q,P/Q,Q/P
These are defined examples of a cell with potential change in a limited system of quantum field fractal polarization point to point functions. Potential change can be factored of a cell stem to multiple degrees of that cell, stem, or system in systems of a quantum field.
Array of sets scales of ratio scales and tiers from Y φ p Q bases
∈3⅄10φn : ∈3⅄9φn : ∈3⅄8φn : ∈3⅄7φn : ∈3⅄6φn : ∈3⅄5φn : ∈3⅄4φn : ∈3⅄3φn : ∈3⅄2φn : ∈3⅄1φn : ∈3⅄Yn
∈2⅄10φn : ∈2⅄9φn : ∈2⅄8φn : ∈2⅄7φn : ∈2⅄6φn : ∈2⅄5φn : ∈2⅄4φn : ∈2⅄3φn : ∈2⅄2φn : ∈2⅄1φn : ∈2⅄Yn
∈1⅄10φn : ∈3⅄1φn : ∈1⅄8φn : ∈1⅄7φn : ∈1⅄6φn : ∈1⅄5φn : ∈1⅄4φn : ∈1⅄3φn : ∈1⅄2φn : ∈1⅄1φn : ∈1⅄Yn
∈3⅄nφn/nYn : ∈3⅄nφn/nφn : ∈3⅄nφn/nPn : ∈3⅄nφn/nQn : ∈3⅄nYn/nφn : ∈3⅄nPn/nφn : ∈3⅄nQn/nφn
∈2⅄nφn /nYn : ∈2⅄nφn/nφn : ∈2⅄nφn/nPn : ∈2⅄nφn/nQn : ∈2⅄nYn/nφn : ∈2⅄nPn/nφn : ∈2⅄nQn/nφn
∈1⅄nφn /nYn : ∈2⅄nφn/nφn : ∈2⅄nφn/nPn : ∈2⅄nφn/nQn : ∈1⅄nYn/nφn : ∈1⅄nPn/nφn : ∈1⅄nQn/nφn
EXAMPLES of ∈3⅄nφn
∈3⅄1φn21=(1φn21/1φn21c2)=(1.61803399852/1.618033998521803399852)
and ∈3⅄1φn21=(1φn21c2/1φn21)=(1.618033998521803399852/1.61803399852)
and ∈3⅄1φn21=(1φn21c2/1φn21c3)=(1.618033998521803399852/1.6180339985218033998521803399852)
and ∈3⅄1φn21=(1φn21c3/1φn21c2)=(1.6180339985218033998521803399852/1.618033998521803399852)
and ∈3⅄1φn21=(1φn21/1φn21c3)=(1.61803399852/1.6180339985218033998521803399852)
and ∈3⅄1φn21=(1φn21c3/1φn21)=(1.6180339985218033998521803399852/1.61803399852)
∈3⅄1φn for such that any 1φncn/1φncn is vector path of 3⅄1φn of numeral variables from the 1φn to the degree of cycle stem cell metric variant cn. (1φn21c2/1φn10c3) example where 3⅄1⅄ paths define a later divided by a previous from same set 1φn where (1φn21c2/1φn10c3)=(1.618033998521803399852/1.6176294117629411762941) and a change of f(n) of (/) division to f(1X) where (1φn21c2x1φn10c3)=(1.618033998521803399852 x 1.6176294117629411762941)
f(1+⅄) where (1φn21c2+1φn10c3)=(1.618033998521803399852 + 1.6176294117629411762941)
f(1-⅄) where (1φn21c2-1φn10c3)=(1.618033998521803399852 - 1.6176294117629411762941)
f(⅄)2 where (1φn21c2/1φn10c3)=(1.618033998521803399852/1.6176294117629411762941)(1.6^18033998521803399852/1.61^76294117629411762941)
1⅄, 2⅄, 1X, 1+⅄, 1-⅄, 2-⅄, 3⅄n, ⅄2, ⅄3, ⅄n, ⅄ncn to the degree of cycle stem cell metric variants
Alternate Path of Y divide 2⅄ to 1Θ
1Θn=2⅄(Y1/Y2)
1st tier fibonacci 01 to 10 digit value for basic numerical display of decimal precision laws not applicable to standard definition floating point. 9 bold numbers are also prime numbers in the ten digit base logic that phi prime fibonacci scale bases share in common of the ten digit example shown below. 2 - 3- 5 - 13- 89 - 1597 - 28657 - 514229 - 434894437
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 1346296 2178309 3524578 5702887 9227465 14930352 24157817 39088169 63245986 102334155 165780141 269114296 434894437 704008733 1138903170
then
1Θn1=2⅄(Y1/Y2)=(0/1)=0
1Θn2=2⅄(Y2/Y3)=(1/1)=1
1Θn3=2⅄(Y3/Y4)=(1/2)=0.5
1Θn4=2⅄(Y4/Y5)=(2/3)=0.6 so 1Θn4c2=0.66 and so on for 1Θncn
1Θn5=2⅄(Y5/Y6)=(3/5)=0.6
1Θn6=2⅄(Y6/Y7)=(5/8)=0.625
1Θn7=2⅄(Y7/Y8)=(8/13)=0.615384 so 1Θn7c2=0.615384615384
1Θn8=2⅄(Y8/Y9)=(13/21)=0.619047 so 1Θn8c2=0.619047619047
1Θn9=2⅄(Y9/Y10)=(21/34)=0.61764705882352941
1Θn10=2⅄(Y10/Y11)=(34/55)=0.618
1Θn11=2⅄(Y11/Y12)=(55/89)=0.6179775280878651685393258764044943820224719101123595505
1Θn12=2⅄(Y12/Y13)=(89/144)=0.61805
1Θn13=2⅄(Y13/Y14)=(144/233)=0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566
1Θn14=2⅄(Y14/Y15)=(233/377)=0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257
1Θn15=2⅄(Y15/Y16)=(377/610)=0.618032786885245901639344262295081967213114754098360655737749
1Θn16=2⅄(Y16/Y17)=(610/987)=0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870
1Θn17=2⅄(Y17/Y18)=(987/1597)=0.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129
1Θn18=2⅄(Y18/Y19)=(1597/2584)=0.618034055727554179566563467492260061919504643962848297213622291021671826625386996904024767801857585139318885448916408668730650154798761609907120743
1Θn19=2⅄(Y19/Y20)=(2584/4181)=0.618033963166706529538387945467591485290600334848122458741927768476441042812724228653432193255202104759626883520688830423343697679980865821573786175556087060511839272901219803874671131308299449892370246352547237502989715379095910069361396795025113609184405644582635733078210954317149007414494140157856972016264051662281750777325998564936
1Θn20=2⅄(Y20/Y21)=(4181/6765)=0.61803399852
1Θn21=2⅄(Y21/Y22)=(6765/10946)=0.6180339850173579389731408733784030696144710396491869175954686643522748035812168828795907180705280467750776539375114196966928558377489493879042572629270966563128083318107071076192216334734149460990316097204458249588890919057189841037822035446738534624520372738900054814544125708021194957061940434862050063950301479992691394116572263840672391741275351726658139959802667641147451123698154577014434496619769778914672026310981
1Θn22=2⅄(Y22/Y23)=(10946/17711)=0.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793348766303427248602563378691208853255039241149568065044322737281915193947264411947377336118796228332674609000056462085709446106939190333690926542826492010614872113375868104567782733894190051380497995595957314663203658743153972107729659533623172039975156682287843712946756253175992321156343515329456270114
1Θn23=2⅄(Y23/Y24)=(17711/28657)=0.618033988205325051470844819764804410789684893743238999197403775691803049865652371148410510520989636040060020239383047771923090344418466692256691209826569424573402659036186621069895662490839934396482534808249293366367728652685207802631119796210350001744774400669993369857277454025194542345674704260739086436123809191471542729525072408137627804724849077014342045573507345500226820672087099138081446069023275290504937711553896081236696095194891300554838259413057891614614230380011864465924555954915029486687371322887950587988973025787765641902502006490560770492375335869072128973723697525909899849949401542380570192274138953833269358271975433576438566493352409533447325260843772900164008793662979376766584080678368286980493422200509474124995638063998325016575356806364937013644135813239348152283909690477021321143176187318979655930488187877307464144886066231636249432948319782252154796384827441811773737655721115259796908259762012771748612904351467355270963464424049970338835188610112712426283281571692780123530027567435530585895243744983773598073769061660327319677565690756185225250375126496144048574519314652615416826604320061416058903583766618976166381686847890567749589978015842551558083539798304079282548766444498726314687510904840004187458561607984087657465889660466901629619290225773807446697142059531702550860173779530306731339637784834420909376417629200544369613009037931395470565655860697211850507729350594968070628467739121331611822591338939875074152912028474718218934291796070768049691174931081411173535261890637540566004815577345849181700806085773109536936874062183759639878563701713368461457933489199846459852741040583452559584045782880273580626025054960393621104791150504239801793628083888753184213281222737899989531353595980039780856335275848832745925951774435565481383257144851170743622849565551174233171650905537913947726558955926998639075967477405171511323585860348256970373730676623512579823428830652196670970443521652650312314617719928813204452664270509823079875772062672296472066161845273406148584987961056635377045747984785567226157657814844540600900303590745716578846355166277000383850368147398541368601039885542799316048434937362599015947238022123739400495515929790278117039466796943155250026171616010049900547859161810377918135185120563911086296541857137872073140942876086122064417070872736155215130683602610182503402310081306487071221691035349129357574065673308441218550441427923369508322573891195868374219213455700177966988868339323725442300310569843319258819834595386816484628537530097358411557385630038036081934605855462888648497749241023135708552884112084307499040374079631503646578497400286143001709878912656593502460131904944690651498761210175524304707401333007642111874934570959974875248630352095474055204662037198590222284258645357155319817147642809784694838957322818159611962173290993474543741494224796733782321945772411627176606064835816728896953623896430191576229193565272010329064451966360749555082527829151690686394249223575391701852950413511532958788428656174756603971106535924904909795163485361342778378755626897442160728617789719789231252399064800921240883553756499284642495725302718358516243849670237638273371253096974561189238231496667480894720312663572600062811878424119761314861988344907003524444289353386607111700457130892975538262902606692954600970094566772516313640646264438008165544195135568970932058484837910458177757615940258924521059427016086819974177338870084098126112293680427120773284014376941061520745367623966221167603028928359563108490072233660187737725512091286596643054053110932756394598178455525700526921869002337997696897791115608751788393760686743204103709390375824405904316571867257563597026904421258331297763199218341068499842970303939700596712845029137732491188889276616533482220748857172767561154342743483267613497574763583068709215898384338904979586139512161077572669853787905223854555605960149352688697351432459782950064556652824789754684719265798932198066789964057647346198136580940084447080992427679101092228774819415849530655686219771783508392364867222668109013504553861185748682695327494155005757755522210978120529015598283141989740726524060438985239208570331856091007432738946854171755592001954147328750392574240150748508217887427155668772027776808458666294448127857068081097114143141291830966256063091042328226960254039152737551034651219597306068325365530236940363610985099626618278256621418850542624838608367938025613288201835502669504833025089855881634504658547649788882297518930802247269428062951460376173360784450570541229019087831943329727466238615347035628293261681264612485605611194472554698677461004292145025648183689848902536901978574170359772481418152632864570611019995114631678124018564399623128729455281432110828069930557978853334263879680357329797257214642146770422584359842272394179432599364902118156122413371951006734829186586174407649090972537250933454304358446452873643437903479080154935966779495411243326237917437275360295913738353630875527794256202672994381826429842621349059566598038873573646927452280420141675681334403461632410929266845796838468785985972013818613253306347489269637435879540775377743657745053564574100568796454618417838573472450012213420804689953589000942178176361796419722929825173605052866664340300799106675506856963394633073943539100394319014551418501587744704609693966570122483162927033534563980877272568656872666364239103883867815891405241302299612660083051261471891684405206406811599260215654115922811180514359493317514045433925393446627351083504902816065882681369298949645810796663991345918972676832885507903828035035069965453466866734131276825906410301148061555640855637366088564748578008863453955403566318874969466447988275116027497644554559095508950692675437065987367833339149248002233311232857591513417315141152249014202463621453746030638238475765083574693792092682416163590047806818578357818334089402240290330460271486896744250968349792371846320270788986983982971001849460864710192972048714101266706214886415186516383431622291237742959835293296576752625885473008340021635202568307917786230240429912412325086366332833164671807935233974247129846110897860906584778588128554977841365111491084202812576333880029312209931255888613602261227623268311407335031580416652126879994416721917856021216456712147119377464493840946365634923404403810587291063265519768293959591024880482953554105454164776494399274173849321282758139372579125519070384199323027532540042572495376347838224517569878214746833234462783962033709041420944271905642600411766758558118435286317479149945911993579230205534424398925218969187284084167917088320480161915064382175384722755347733538053529678612555396587221272289492968559165299926719475171860278465994346930941829221481662421048958369682800013958195205359946958858219632201556338765397634085912691488990473531772341836200579265101022437798792616114736364588058764001814565376696793104651568552186202324039501692431168649893568761559130404438706075304463132916913843040094915727396447639320235893498970583103604703911784206302125135220016051924486163939002686952577031789789580207279198799595212339044561538193111630666154866175803468611508531946819276267578602086750183201312070349303835014132672645426946295843947377604075792999965104511986600132602854450919496109153086505914785218271277523816170569145409498551837247443905503018459713159088529853089995463586558258017238371078619534494189901245768922078375266078096102173988903234811738842167707715392399762710681508880901699410266252573542240988240220539484244687161949959870188784590152493282618557420525526049481802003001011969152388596154517220923334612834560491328471228670132951809331053494783124541996719824126740412464668318386432634260390131555989810517500087238720033499668492863872701259727117283735213036954321806190459573577136476253620406881390236242453850717102278675367275011341033604354956904072303451163764525246885577694804061834804759744565027741912970652894580730711519000593223296227797745751474334368566144397529399448651289388282095125100324528038524618766793453606448686184876295494992497470077119028509613706947691663467913598771678821928324667620476672366263042188645008200439683148968838329204033918414349024671110025473706249781903199916250828767840318246850682206790661967407614195484523851066057158809365948982796524409393865373207244303311581812471647415989112607739819241372090588686882786055762989845412988100638587430645217573367763548173221202498516941759430505635621314164078584639006176501378371776529294762187249188679903688453083016365983878284537809261262518756324807202428725965732630770841330216003070802945179188330948808319084342394528387479498900792127577904176989915203964127438322224936315734375545242000209372928080399204382873294483023345081480964511288690372334857102976585127543008688976515336566981889241721045468820881460027218480650451896569773528282793034860592525386467529748403531423386956066580591129566946993753707645601423735910946714589803538402484558746554070558676763094531877028300240778867292459085040304288655476846843703109187981993928185085668423072896674459992322992637052029172627979202289144013679031301252748019681055239557525211990089681404194437659210664061136894999476567679799001989042816763792441637296297588721778274069162857242558537181142478277558711658582545276895697386327947796349931953798373870258575566179293017412848518686533831175628991171441532609833548522176082632515615730885996440660222633213525491153993788603133614823603308092263670307429249398052831768852287399239278361307882890742227030045015179537285828942317758313850019192518407369927068430051994277139965802421746868129950797361901106186970024775796489513905851973339847157762501308580800502495027392958090518895906759256028195554314827092856893603657047143804306103220853543636807760756534180130509125170115504065324353561084551767456467878703283665422060927522071396168475416128694559793418710960672785008898349443416966186272115015528492165962940991729769340824231426876504867920577869281501901804096730292773144432424887462051156785427644205604215374952018703981575182328924870014307150085493945632829675123006595247234532574938060508776215235370066650382105593746728547998743762431517604773702760233101859929511114212932267857765990857382140489234741947866140907980598108664549673727187074711239836689116097288620581358830303241790836444847681194821509578811459678263600516453222598318037477754126391457584534319712461178769585092647520675576647939421432808737830198555326796245245489758174268067138918937781344872108036430889485989461562619953240046062044177687824964232124786265135917925812192483511881913668562654848728059461911574833374044736015633178630003140593921205988065743099417245350176222214467669330355585022856544648776913145130334647730048504728338625815682032313221900408277209756778448546602924241895522908887880797012946226052971350804340998708866943504204906305614684021356038664200718847053076037268381198311058380151446417978155424503611683009386886275604564329832152702655546637819729908922776285026346093450116899884844889555780437589419688034337160205185469518791220295215828593362878179851345221062916564888159960917053424992148515196985029835642251456886624559444463830826674111037442858638378057717137174163380674878738179153435460794919216945248979306975608053878633492689395261192727780298007467634434867571622989147503227832641239487734235963289946609903339498202882367309906829047004222354049621383955054611438740970792476532784310988589175419618243361133405450675227693059287434134766374707750287887776110548906026450779914157099487036326203021949261960428516592804550371636947342708587779600097707366437519628712007537425410894371357783438601388840422933314722406392853404054855707157064591548312803154552116411348012701957636877551732560979865303416268276511847018180549254981330913912831070942527131241930418396901280664410091775133475241651254492794081725232927382489444114875946540112363471403147573018808668039222528527061450954391597166486373311930767351781414663084063230624280280559723627734933873050214607251282409184492445126845098928708517988624070907631643228530550999755731583906200928219981156436472764071605541403496527898942666713193984017866489862860732107338521129217992113619708971629968245105907806120668597550336741459329308720382454548626862546672715217922322643682171895173954007746798338974770562166311895871863768014795686917681543776389712810133649719091321492131067452978329901943678682346372614021007083784066720173081620546463342289841923439299298600690930662665317374463481871793977038768887182887252678228705028439822730920891928673622500610671040234497679450047108908818089820986146491258680252643333217015039955333775342848169731653697176955019715950727570925079387235230484698328506124158146351676728199043863628432843633318211955194193390794570262065114980633004152563073594584220260320340579963010782705796140559025717974665875702271696269672331367554175245140803294134068464947482290539833199567295948633841644275395191401751753498272673343336706563841295320515057403077782042781868304428237428900443172697770178315943748473322399413755801374882227727954775447534633771853299368391666957462400111665561642879575670865757057612450710123181072687301531911923788254178734689604634120808179502390340928917890916704470112014516523013574344837212548417489618592316013539449349199148550092473043235509648602435705063335310744320759325819171581114561887147991764664828837631294273650417001081760128415395889311512021495620616254318316641658233590396761698712356492305544893045329238929406427748892068255574554210140628816694001465610496562794430680113061381163415570366751579020832606343999720836095892801060822835607355968873224692047318281746170220190529364553163275988414697979551244024147677705272708238824719963708692466064137906968628956275953519209966151376627002128624768817391911225878493910737341661723139198101685452071047213595282130020588337927905921764315873957497295599678961510276721219946260948459364204208395854416024008095753219108769236137767386676902676483930627769829361063614474648427958264996335973758593013923299717346547091461074083121052447918484140000697909760267997347942910981610077816938269881704295634574449523676588617091810028963255051121889939630805736818229402938200090728268834839655232578427609310116201975084621558432494678438077956520221935303765223156645845692152004745786369822381966011794674948529155180235195589210315106256761000802596224308196950134347628851589489479010363959939979760616952228076909655581533307743308790173430575426597340963813378930104337509160065603517465191750706633632271347314792197368880203789649998255225599330006630142722545974805457654325295739260913563876190808528457270474927591862372195275150922985657954426492654499773179327912900861918553930976724709495062288446103918763303904805108699445161740586942108385385769619988135534075444045084970513312628677112049412011026974212234358097497993509439229507624664130927871026276302474090100150050598457619429807725861046166730641728024566423561433506647590466552674739156227099835991206337020623233415919321631713019506577799490525875004361936001674983424643193635062986355864186760651847716090309522978678856823812681020344069511812122692535855113933768363750567051680217747845203615172558188226262344278884740203091740237987228251387095648532644729036535575950029661164811389887287573716718428307219876469972432564469414104756255016226401926230938339672680322434309243814774749624873503855951425480685347384583173395679938583941096416233381023833618313152109432250410021984157448441916460201695920717451233555501273685312489095159995812541438392015912342534110339533098370380709774226192553302857940468297449139826220469693268660362215165579090623582370799455630386990962068604529434344139302788149492270649405031929371532260878668388177408661060124925847087971525281781065708203929231950308825068918588826464738109362459433995184422654150818299193914226890463063125937816240360121436298286631538542066510800153540147258959416547440415954217119726419373974945039606378895208849495760198206371916111246815786718777262100010468646404019960219143664724151167254074048225564434518616742855148829256377150434448825766828349094462086052273441044073001360924032522594828488676414139651743029626269323376487420176571169347803329029556478347349687685382280071186795547335729490176920124227937327703527933838154726593851415012038943364622954252015214432773842342185155459399099696409254283421153644833722999616149631852601458631398960114457200683951565062637400984052761977876260599504484070209721882960533203056844749973828383989950099452140838189622081864814879436088913703458142862127926859057123913877935582929127263844784869316397389817496597689918693512928778308964650870642425934326691558781449558572076630491677426108804131625780786544299822033011131660676274557699689430156680741180165404613183515371462469902641588442614369961963918065394144537111351502250758976864291447115887915692500959625920368496353421502599713856998290121087343406497539868095055309348501238789824475695292598666992357888125065429040025124751369647904525944795337962801409777715741354642844680182852357190215305161042677181840388037826709006525456258505775203266217678054227588372823393935164183271103046376103569808423770806434727989670935548033639250444917472170848309313605750776424608298147049586488467041211571343825243396028893464075095090204836514638657221621244373102557839271382210280210768747600935199078759116446243500715357504274697281641483756150329762361726628746903025438810761768503332519105279687336427399937188121575880238685138011655092996475555710646613392888299542869107024461737097393307045399029905433227483686359353735561991834455804864431029067941515162089541822242384059741075478940572983913180025822661129915901873887706319572879226715985623058938479254632376033778832396971071640436891509927766339812262274487908713403356945946889067243605401821544474299473078130997662002303102208884391248211606239313256795896290609624175594095683428132742436402973095578741668702236800781658931500157029696060299403287154970862267508811110723383466517779251142827232438845657256516732386502425236416931290784101615661095020413860487838922427330146212094776145444394039850647311302648567540217049935443347175210245315280734201067801933210035942352653801863419059915552919007572320898907771225180584150469344313780228216491607635132777331890986495446138814251317304672505844994242244477789021879470984401716858010259273475939561014760791429668143908992567261053145828244407998045852671249607425759849251491782112572844331227972223191541333705551872142931918902885856858708169033743936908957671773039745960847262448965348780402693931674634469763059636389014900373381721743378581149457375161391632061974386711798164497330495166974910144118365495341452350211117702481069197752730571937048539623826639215549429458770980912168056670272533761384652964371706738318735387514394388805527445301322538995707854974351816310151097463098021425829640227518581847367135429388980004885368321875981435600376871270544718567889171930069442021146665736120319642670202742785357853229577415640157727605820567400635097881843877586628048993265170813413825592350909027462749066545695641553547126356562096520919845064033220504588756673762082562724639704086261646369124472205743797327005618173570157378650940433401961126426353072547719579858324318665596538367589070733154203161531214014027986181386746693652510730362564120459224622256342254946435425899431203545381582161426527549987786579195310046410999057821823638203580277070174826394947133335659699200893324493143036605366926056460899605680985448581498412255295390306033429877516837072966465436019122727431343127333635760896116132184108594758697700387339916948738528108315594793593188400739784345884077188819485640506682485954566074606553372648916495097183934117318630701050354189203336008654081027323167114492096171964964930034546533133265868723174093589698851938444359144362633911435251421991136546044596433681125030533552011724883972502355445440904491049307324562934012632166660850751997766688767142408486582684858847750985797536378546253969361761524234916425306207907317583836409952193181421642181665910597759709669539728513103255749031650207628153679729211013016017028998150539135289807027951285898733293785113584813483616568377708762257040164706703423247374114526991659978364797431692082213769759570087587674913633667166835328192064766025752870153889102139093415221411871445022158634888508915797187423666119970687790068744111386397738772376731688592664968419583347873120005583278082143978783543287852880622535506159053634365076595596189412708936734480231706040408975119517046445894545835223505600725826150678717241860627420874480929615800676972467459957427504623652161775482430121785253166765537216037966290958579055728094357399588233241441881564713682520850054088006420769794465575601074781030812715915832082911679519838084935617824615277244652266461946470321387444603412778727710507031440834700073280524828139721534005653069058170778518337578951041630317199986041804794640053041141780367798443661234602365914087308511009526468227658163799420734898977562201207383885263635411941235998185434623303206895348431447813797675960498307568831350106431238440869595561293924695536867083086156959905084272603552360679764106501029416896395296088215793697874864779983948075513836060997313047422968210210419792720801200404787660955438461806888369333845133824196531388491468053180723732421397913249816798687929650696164985867327354573053704156052622395924207000034895488013399867397145549080503890846913494085214781728722476183829430854590501448162752556094496981540286840911470146910004536413441741982761628921380465505810098754231077921624733921903897826011096765188261157832292284607600237289318491119098300589733747426457759011759779460515755312838050040129811215409847506717381442579474473950518197996998988030847611403845482779076665387165439508671528771329867048190668946505216875458003280175873259587535331681613567365739609868444010189482499912761279966500331507136127298740272882716264786963045678193809540426422863523746379593118609763757546149282897721324632724988658966395645043095927696548836235474753114422305195938165195240255434972258087029347105419269288480999406776703772202254248525665631433855602470600551348710611717904874899675471961475381233206546393551313815123704505007502529922880971490386293052308336532086401228321178071675332379523327633736957811354991799560316851031161670795966081585650975328889974526293750218096800083749171232159681753149317793209338032592385804515476148933942841190634051017203475590606134626792755696688418187528352584010887392260180758627909411313117213944237010154587011899361412569354782426632236451826778797501483058240569494364378685835921415360993823498621628223470705237812750811320096311546916983634016121715462190738737481243675192797571274034267369229158669783996929197054820811669051191680915657605471612520501099207872422095823010084796035872561677775063684265624454757999790627071919600795617126705516976654918519035488711309627665142897023414872456991311023484663433018110758278954531179118539972781519349548103430226471717206965139407474613532470251596468576613043933419408870433053006246292354398576264089053285410196461597515441253445929441323236905468122971699759221132707540914959695711344523153156296890812018006071814914331576927103325540007677007362947970827372020797710855986320968698747251980318944760442474788009910318595805562340789335938863105000523432320200998010957183236207558362703702411278221725930837142757441462818857521722441288341417454723104302613672052203650068046201626129741424433820706982587151481313466168824371008828558467390166451477823917367484384269114003559339777366786474508846006211396866385176396691907736329692570750601947168231147712600760721638692117109257772969954984820462714171057682241686149980807481592630072931569948005722860034197578253131870049202638098893813029975224203510486094148026660152842237498691419199497504972607041909481104093240743971804445685172907143106396342952856195693896779146456363192239243465819869490874829884495934675646438915448232543532121296716334577939072477928603831524583871305440206581289039327214991101650556583033813727884984471507834037059008270230659175768573123495132079422130718498098195903269707226855567575112537948843214572355794395784625047981296018424817671075129985692849914506054367170324876993404752765467425061939491223784764629933349617894406253271452001256237568482395226297239766898140070488885787067732142234009142617859510765258052133859092019401891335450326272812925288760163310883902711379418641169696758209163555152318805178490421188540321736399483546777401681962522245873608542415465680287538821230414907352479324423352060578567191262169801444673203754754510241825731932861081062218655127891963569110514010538437380046759953937955822312175035767875213734864082074187807516488118086331437345151271940538088425166625955263984366821369996859406078794011934256900582754649823777785532330669644414977143455351223086854869665352269951495271661374184317967686778099591722790243221551453397075758104477091112119202987053773947028649195659001291133056495795093694385315978643961335799281152946923962731618801688941619848553582021844575496388316990613113724395435670167847297344453362180270091077223714973653906549883100115155110444219562410580311965662839794814530481208779704784171406637121820148654778937083435111840039082946575007851484803014970164357748543113375440555536169173325888962557141361621942282862825836619325121261820846564539205080783054751020693024391946121366507310604738807272219701992532365565132428377010852496772167358760512265764036710053390096660501797117632690093170952995777645950378616044945388561259029207523467215689011410824580381756638866594549324772306940712565865233625292249712112223889451093973549220085842900512963673796978050738039571483407195449628363052657291412220399902292633562480371287992462574589105628642216561398611159577066685277593607146595945144292842935408451687196845447883588651987298042363122448267439020134696583731723488152981819450745018669086087168929057472868758069581603098719335589908224866524758348745507205918274767072617510555885124053459887636528596852426981191331960777471472938549045608402833513626688069232648218585336915936769375719719440276372265066126949785392748717590815507554873154901071291482011375929092368356771469449000244268416093799071780018843563527235928394458596503472101057333286806015982133510137139267892661478870782007886380291028370031754894092193879331402449663258540670691279617545451373137453327284782077677356317828104826045992253201661025229437833688104128136231985204313082318456223610287189866350280908678507868932547021670098056321317653627385978992916215933279826918379453536657710158076560700701399309069337334682625536518128206022961231112817112747321771294971560177269079108071326377499389328959765502320549952891091181910179013853508741319747356666782984960044666224657151830268346302823044980284049272429074920612764769515301671493875841853648323271800956136371567156366681788044805806609205429737934885019366995847436926405415779739679659420036989217294203859440974282025334124297728303730327668632445824754859196705865931535052517709460166800432704051366158355724604808598248246501727326656663293436158704679484942596922217957218131695571762571099556827302229821684056251526677600586244198625117772272045224552465366228146700631608333042537599888334438357120424329134242942387549289876818927312698468088076211745821265310395365879191820497609659071082109083295529887985483476986425655162787451582510381407683986460550650800851449907526956764490351397564294936664689255679240674180828418885438112852008235335171162368705726349582998918239871584604110688487978504379383745681683358341766409603238301287643507694455106954670761070593572251107931744425445789859371183305998534389503437205569319886938618836584429633248420979167393656000279163904107198939177164392644031126775307952681718253829779809470635446836724011585302020448755975852322294727291761175280036291307533935862093031371043724046480790033848623372997871375231182608088774121506089262658338276860801898314547928952786404717869979411662072094078235684126042502704400321038489723278780053739051540635795791604145583975991904246780891230763862232613323097323516069372230170638936385525351572041735003664026241406986076700282653452908538925916878947552081515859999302090239732002652057089018389922183061730118295704365425550476323411382908189971036744948878110060369194263181770597061799909271731165160344767421572390689883798024915378441567505321561922043479778064696234776843354154307847995254213630177
1Θn24=2⅄(Y24/Y25)=(28657/46368)=0.61803398895790200138026224982746721877156659765355417529330572808833678
1Θn25=2⅄(Y25/Y26)=(46368/75025)=0.61803398867044318560479840053315561479506831056314561812729090303232255914695101632789070309896701099633455514828390536487837387537487504165278240586471176274575141619460179940019993335554815061646117960679773408863712095968010663112295901366211262912362545818060646451182939020326557814061979340219926691102965678107297567477507497500833055648117294235254915028323892035988003998667110963012329223592135954681772742419193602132622459180273242252582472509163612129290236587804065311562812395868043985338220593135621459513495501499500166611129623458847050983005664778407197600799733422192602465844718427190936354548483838720426524491836054648450516494501832722425858047317560813062312562479173608797067644118627124291902699100299900033322225924691769410196601132955681439520159946684438520493168943685438187270909696767744085304898367210929690103298900366544485171609463512162612462512495834721759413528823725424858380539820059980006664445184938353882039320226591136287904031989336887704098633788737087637454181939353548817060979673442185938020659780073308897034321892702432522492502499166944351882705764745084971676107964011996001332889036987670776407864045318227257580806397867377540819726757747417527490836387870709763412195934688437187604131956014661779406864378540486504498500499833388870376541152949016994335221592802399200266577807397534155281572809063645451516161279573475508163945351549483505498167277574141952682439186937687437520826391202932355881372875708097300899700099966677774075308230589
1Θn26=2⅄(Y26/Y27)=(75025/121393)=0.6180339887802426828565073768668704126267577207911494072969611097839249380112527081462687304869308773982025322712182745298328569192622309358859242295684265155321970789089980476633743296565699834422083645679734416317250582817790152644715922664404043066733666685887983656388753882019556317085828672163963325727183610257593106686547000238893511157974512533671628512352442068323544191180710584630085754532798431540533638677683227204204525796380351420592620661817402980402494377764780506289489509279777252395113392040727224798793999654016294185002430123647986292455083901048660136910695015363324079642153995699916799156458774393910686777656042770176204558747209476658456418409628232270394503801701910324318535665153674429332828087286746352755101200233950886789188832964009456887958943266909953621708006227706704669956257774336246735808489781124117535607489723460166566441228077401497615183742060909607638002191230136828317942550229420147784468626691819132898931569365614162266358027233860272009094428838565650408178395788884037794601006647829776016739021195620834809255887901279315940787360061947558755447183939765884359065184977717001804057894606773042926692642903627062515960557857537090277034095870437339879564719547255607819231751418945079205555509790515103836300280905818292652788875800087319697181880339064031698697618478824973433394017776972313065827518884943942401950689084214081536826670401093967526957897078085227319532427734712874712709958564332375013386274332127882167835048149399059253828474458988574300000823770728130946594943695270732249800235598428245450726153896847429423442867381150478198907680014498364815104660071009036764887596484146532337119932780308584514757852594465908248416300775168255171220745842017249759047062021698120978969133310816933431087459738205662599985172126893642961291013485126819503595759228291581886929229856746270378028387139291392419661759739029433328116118721837338232023263285362417931841209954445478734358653299613651528506586046971406918026574843689504337152883609433822378555600405295198240425724712298073200266901715914426696761757267717248935276333890751526035273862578567133195489031492754936446088324697470200093909863006927911823581260863476477226858220819981382781544240606954272486881451154514675475521652813588921931248095030191197185999192704686431672336955178634682395195769113540319458288369181089519165025989966472531365070473585791602481197433130411143970410155445536398309622465875297587175537304457423409916552025240335109932203669074823095236133879218735841440610249355399405237534289456558450652014531315644229897934806784575716886476155956274249750809354740388655029532180603494435428731475455751155338446203652599408532617201980344830426795614244643430840328519766378621502063545673968021220333956653184285749590174062754854069015511602810705724382789781947888263738436318403861837173477877637096043429192787063504485431614673004209468420749137100162282833441796479203907968334253210646412890364353793052317678943596418244874086644205184812962856177868575
1Θn27=2⅄(Y27/Y28)=(121393/196418)
1Θn28=2⅄(Y28/Y29)=(196418/317811)
1Θn29=2⅄(Y29/Y30)=(317811/514229)
1Θn30=2⅄(Y30/Y31)=(514229/832040)
1Θn31=2⅄(Y31/Y32)=(832040/1346296)
1Θn32=2⅄(Y32/Y33)=(1346296/2178309)
1Θn33=2⅄(Y33/Y34)=(2178309/3524578)
1Θn34=2⅄(Y34/Y35)=(3524578/5702887)
1Θn35=2⅄(Y35/Y36)=(5702887/9227465)
1Θn36=2⅄(Y36/Y37)=(9227465/14930352)
1Θn37=2⅄(Y37/Y38)=(14930352/24157817)
1Θn38=2⅄(Y38/Y39)=(24157817/39088169)
1Θn39=2⅄(Y39/Y40)=(39088169/63245986)
1Θn40=2⅄(Y40/Y41)=(63245986/102334155)
1Θn41=2⅄(Y41/Y42)=(102334155/165780141)
1Θn42=2⅄(Y42/Y43)=(165780141/269114296)
1Θn43=2⅄(Y43/Y44)=(269114296/434894437)
1Θn44=2⅄(Y44/Y45)=(434894437/704008733)
1Θn45=2⅄(Y45/Y46)=(704008733/1138903170)
And so on for 1Θn45 1Θn46 . . . of ∈1Θn
Similar decimal cycle stem variants from different functions of y base minus or plus 1
1φn8 : 1Θn7 variables of Y base are 1.615384 : 0.615384
1φn9 : 1Θn8 variables of Y base are 1.619047 : 0.619047
Significant whole number one variable difference from alternate stem paths 1⅄ and 2⅄ of Y between 1φn : 1Θn
Now from 1Θn paths 2Θn are factorable in 1⅄ 2⅄ 3⅄ for sets ∈1⅄2Θn, ∈2⅄2Θn, and ∈3⅄2Θn
With path variable set ratios 1φn and 1Θn then Y can be again divided with 1φn and 1Θn in 1⅄ 2⅄ 3⅄ for (1Θn/Yn) and (Yn/1Θn) functions as with P variables (ᐱ)T,S. More complex ratio sets (ᐱ)D,B,O,G, and (ᐱ)E,F,I,H then require definition of Q and the path of Q from Prime P paths 1⅄ and 2⅄ for D, B, O, G, E, F, I, H, T, and S variables.
D=∈1⅄(φ/Θ)cn
B=∈2⅄(φ/Θ)cn
O=∈1⅄(Θ/φ)cn
G=∈2⅄(Θ/φ)cn
E=∈1⅄(Θ/Q)cn
F=∈2⅄(Θ/Q)cn
I= ∈1⅄(Q/Θ)cn
H=∈2⅄(Q/Θ)cn
T=∈(Θ/P)cn
S=∈(P/Θ)cn
Alternate Path of divide 1⅄ to 2Θ for 1⅄2Θ from 1Θ of 2⅄(Yn1/Yn2)
1⅄2Θn=(1Θn2/1Θn1) and of cn variable paths in later divided by previous division functions
so
1⅄2Θn1=(1Θn2/1Θn1)=(1/1)/(0/1)=(1/0)=0
1⅄2Θn2=(1Θn3/1Θn2)=(1/2)/(1/1)=(0.5/1)=0.5
1⅄2Θn3=(1Θn4/1Θn3)=(2/3)/(1/2)=(0.6/0.5)=1.2 and 1⅄2Θn3=(1Θn4c2/1Θn3)=(2/3)/(1/2)=(0.66/0.5)=1.32 and 1⅄2Θn3=(1Θn4c3/1Θn3)=(2/3)/(1/2)=(0.666/0.5)=1.332
1⅄2Θn4=(1Θn5/1Θn4)=(3/5)/(2/3)=(0.6/0.6)=1 and 1⅄2Θn4=(1Θn5/1Θn4c2)=(3/5)/(2/3)=(0.6/0.66)=0.09 and 1⅄2Θn4=(1Θn5/1Θn4c3)=(3/5)/(2/3)=(0.6/0.666)=0.009
1⅄2Θn5=(1Θn6/1Θn5)=(5/8)/(3/5)=(0.625/0.6)=1.0416
1⅄2Θn6=(1Θn7/1Θn6)=(8/13)/(5/8)=(0.615384/0.625)=0.9878144 and 1⅄2Θn6=(1Θn7c2/1Θn6)=(8/13)/(5/8)=(0.615384615384/0.625)=0.9878153846144 and
1⅄2Θn7=(1Θn8/1Θn7)=(13/21)/(8/13)=(0.619047/0.615384)=1.00595237770
1⅄2Θn8=(1Θn9/1Θn8)=(21/34)/(13/21)=(0.61764705882352941/0.619047)
1⅄2Θn9=(1Θn10/1Θn9)=(34/55)/(21/34)=(0.618/0.61764705882352941)
1⅄2Θn10=(1Θn11/1Θn10)=(55/89)/(34/55)=(0.6179775280878651685393258764044943820224719101123595505/0.618)
1⅄2Θn11=(1Θn12/1Θn11)=(89/144)/(55/89)=(0.6180^5/0.6179775280878651685393258764044943820224719101123595505)
1⅄2Θn12=(1Θn13/1Θn12)=(144/233)/(89/144)=(0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566/0.61805)
1⅄2Θn13=(1Θn14/1Θn13)=(233/377)/(144/233)=(0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566)
1⅄2Θn14=(1Θn15/1Θn14)=(377/610)/(233/377)=(0.618032786885245901639344262295081967213114754098360655737749/0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257)
1⅄2Θn15=(1Θn16/1Θn15)=(610/987)/(377/610)=(0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870/0.618032786885245901639344262295081967213114754098360655737749)
1⅄2Θn16=(1Θn17/1Θn16)=(987/1597)/(610/987)=(0.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870)
1⅄2Θn17=(1Θn18/1Θn17)=(1597/2584)/(987/1597)=(0.618034055727554179566563467492260061919504643962848297213622291021671826625386996904024767801857585139318885448916408668730650154798761609907120743/0.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129)
1⅄2Θn18=(1Θn19/1Θn18)=(2584/4181)/(1597/2584)=(0.618033963166706529538387945467591485290600334848122458741927768476441042812724228653432193255202104759626883520688830423343697679980865821573786175556087060511839272901219803874671131308299449892370246352547237502989715379095910069361396795025113609184405644582635733078210954317149007414494140157856972016264051662281750777325998564936/0.618034055727554179566563467492260061919504643962848297213622291021671826625386996904024767801857585139318885448916408668730650154798761609907120743)
1⅄2Θn19=(1Θn20/1Θn19)=(4181/6765)/(2584/4181)=(0.61803399852/0.618033963166706529538387945467591485290600334848122458741927768476441042812724228653432193255202104759626883520688830423343697679980865821573786175556087060511839272901219803874671131308299449892370246352547237502989715379095910069361396795025113609184405644582635733078210954317149007414494140157856972016264051662281750777325998564936)
1⅄2Θn20=(1Θn21/1Θn20)=(6765/10946)/(4181/6765)=(0.6180339850173579389731408733784030696144710396491869175954686643522748035812168828795907180705280467750776539375114196966928558377489493879042572629270966563128083318107071076192216334734149460990316097204458249588890919057189841037822035446738534624520372738900054814544125708021194957061940434862050063950301479992691394116572263840672391741275351726658139959802667641147451123698154577014434496619769778914672026310981/0.61803399852)
1⅄2Θn21=(1Θn22/1Θn21)=(10946/17711)/(6765/10946)=(0.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793348766303427248602563378691208853255039241149568065044322737281915193947264411947377336118796228332674609000056462085709446106939190333690926542826492010614872113375868104567782733894190051380497995595957314663203658743153972107729659533623172039975156682287843712946756253175992321156343515329456270114/0.6180339850173579389731408733784030696144710396491869175954686643522748035812168828795907180705280467750776539375114196966928558377489493879042572629270966563128083318107071076192216334734149460990316097204458249588890919057189841037822035446738534624520372738900054814544125708021194957061940434862050063950301479992691394116572263840672391741275351726658139959802667641147451123698154577014434496619769778914672026310981)
1⅄2Θn22=(1Θn23/1Θn22)=(17711/28657)/(10946/17711)=(0.618033988205325051470844819764804410789684893743238999197403775691803049865652371148410510520989636040060020239383047771923090344418466692256691209826569424573402659036186621069895662490839934396482534808249293366367728652685207802631119796210350001744774400669993369857277454025194542345674704260739086436123809191471542729525072408137627804724849077014342045573507345500226820672087099138081446069023275290504937711553896081236696095194891300554838259413057891614614230380011864465924555954915029486687371322887950587988973025787765641902502006490560770492375335869072128973723697525909899849949401542380570192274138953833269358271975433576438566493352409533447325260843772900164008793662979376766584080678368286980493422200509474124995638063998325016575356806364937013644135813239348152283909690477021321143176187318979655930488187877307464144886066231636249432948319782252154796384827441811773737655721115259796908259762012771748612904351467355270963464424049970338835188610112712426283281571692780123530027567435530585895243744983773598073769061660327319677565690756185225250375126496144048574519314652615416826604320061416058903583766618976166381686847890567749589978015842551558083539798304079282548766444498726314687510904840004187458561607984087657465889660466901629619290225773807446697142059531702550860173779530306731339637784834420909376417629200544369613009037931395470565655860697211850507729350594968070628467739121331611822591338939875074152912028474718218934291796070768049691174931081411173535261890637540566004815577345849181700806085773109536936874062183759639878563701713368461457933489199846459852741040583452559584045782880273580626025054960393621104791150504239801793628083888753184213281222737899989531353595980039780856335275848832745925951774435565481383257144851170743622849565551174233171650905537913947726558955926998639075967477405171511323585860348256970373730676623512579823428830652196670970443521652650312314617719928813204452664270509823079875772062672296472066161845273406148584987961056635377045747984785567226157657814844540600900303590745716578846355166277000383850368147398541368601039885542799316048434937362599015947238022123739400495515929790278117039466796943155250026171616010049900547859161810377918135185120563911086296541857137872073140942876086122064417070872736155215130683602610182503402310081306487071221691035349129357574065673308441218550441427923369508322573891195868374219213455700177966988868339323725442300310569843319258819834595386816484628537530097358411557385630038036081934605855462888648497749241023135708552884112084307499040374079631503646578497400286143001709878912656593502460131904944690651498761210175524304707401333007642111874934570959974875248630352095474055204662037198590222284258645357155319817147642809784694838957322818159611962173290993474543741494224796733782321945772411627176606064835816728896953623896430191576229193565272010329064451966360749555082527829151690686394249223575391701852950413511532958788428656174756603971106535924904909795163485361342778378755626897442160728617789719789231252399064800921240883553756499284642495725302718358516243849670237638273371253096974561189238231496667480894720312663572600062811878424119761314861988344907003524444289353386607111700457130892975538262902606692954600970094566772516313640646264438008165544195135568970932058484837910458177757615940258924521059427016086819974177338870084098126112293680427120773284014376941061520745367623966221167603028928359563108490072233660187737725512091286596643054053110932756394598178455525700526921869002337997696897791115608751788393760686743204103709390375824405904316571867257563597026904421258331297763199218341068499842970303939700596712845029137732491188889276616533482220748857172767561154342743483267613497574763583068709215898384338904979586139512161077572669853787905223854555605960149352688697351432459782950064556652824789754684719265798932198066789964057647346198136580940084447080992427679101092228774819415849530655686219771783508392364867222668109013504553861185748682695327494155005757755522210978120529015598283141989740726524060438985239208570331856091007432738946854171755592001954147328750392574240150748508217887427155668772027776808458666294448127857068081097114143141291830966256063091042328226960254039152737551034651219597306068325365530236940363610985099626618278256621418850542624838608367938025613288201835502669504833025089855881634504658547649788882297518930802247269428062951460376173360784450570541229019087831943329727466238615347035628293261681264612485605611194472554698677461004292145025648183689848902536901978574170359772481418152632864570611019995114631678124018564399623128729455281432110828069930557978853334263879680357329797257214642146770422584359842272394179432599364902118156122413371951006734829186586174407649090972537250933454304358446452873643437903479080154935966779495411243326237917437275360295913738353630875527794256202672994381826429842621349059566598038873573646927452280420141675681334403461632410929266845796838468785985972013818613253306347489269637435879540775377743657745053564574100568796454618417838573472450012213420804689953589000942178176361796419722929825173605052866664340300799106675506856963394633073943539100394319014551418501587744704609693966570122483162927033534563980877272568656872666364239103883867815891405241302299612660083051261471891684405206406811599260215654115922811180514359493317514045433925393446627351083504902816065882681369298949645810796663991345918972676832885507903828035035069965453466866734131276825906410301148061555640855637366088564748578008863453955403566318874969466447988275116027497644554559095508950692675437065987367833339149248002233311232857591513417315141152249014202463621453746030638238475765083574693792092682416163590047806818578357818334089402240290330460271486896744250968349792371846320270788986983982971001849460864710192972048714101266706214886415186516383431622291237742959835293296576752625885473008340021635202568307917786230240429912412325086366332833164671807935233974247129846110897860906584778588128554977841365111491084202812576333880029312209931255888613602261227623268311407335031580416652126879994416721917856021216456712147119377464493840946365634923404403810587291063265519768293959591024880482953554105454164776494399274173849321282758139372579125519070384199323027532540042572495376347838224517569878214746833234462783962033709041420944271905642600411766758558118435286317479149945911993579230205534424398925218969187284084167917088320480161915064382175384722755347733538053529678612555396587221272289492968559165299926719475171860278465994346930941829221481662421048958369682800013958195205359946958858219632201556338765397634085912691488990473531772341836200579265101022437798792616114736364588058764001814565376696793104651568552186202324039501692431168649893568761559130404438706075304463132916913843040094915727396447639320235893498970583103604703911784206302125135220016051924486163939002686952577031789789580207279198799595212339044561538193111630666154866175803468611508531946819276267578602086750183201312070349303835014132672645426946295843947377604075792999965104511986600132602854450919496109153086505914785218271277523816170569145409498551837247443905503018459713159088529853089995463586558258017238371078619534494189901245768922078375266078096102173988903234811738842167707715392399762710681508880901699410266252573542240988240220539484244687161949959870188784590152493282618557420525526049481802003001011969152388596154517220923334612834560491328471228670132951809331053494783124541996719824126740412464668318386432634260390131555989810517500087238720033499668492863872701259727117283735213036954321806190459573577136476253620406881390236242453850717102278675367275011341033604354956904072303451163764525246885577694804061834804759744565027741912970652894580730711519000593223296227797745751474334368566144397529399448651289388282095125100324528038524618766793453606448686184876295494992497470077119028509613706947691663467913598771678821928324667620476672366263042188645008200439683148968838329204033918414349024671110025473706249781903199916250828767840318246850682206790661967407614195484523851066057158809365948982796524409393865373207244303311581812471647415989112607739819241372090588686882786055762989845412988100638587430645217573367763548173221202498516941759430505635621314164078584639006176501378371776529294762187249188679903688453083016365983878284537809261262518756324807202428725965732630770841330216003070802945179188330948808319084342394528387479498900792127577904176989915203964127438322224936315734375545242000209372928080399204382873294483023345081480964511288690372334857102976585127543008688976515336566981889241721045468820881460027218480650451896569773528282793034860592525386467529748403531423386956066580591129566946993753707645601423735910946714589803538402484558746554070558676763094531877028300240778867292459085040304288655476846843703109187981993928185085668423072896674459992322992637052029172627979202289144013679031301252748019681055239557525211990089681404194437659210664061136894999476567679799001989042816763792441637296297588721778274069162857242558537181142478277558711658582545276895697386327947796349931953798373870258575566179293017412848518686533831175628991171441532609833548522176082632515615730885996440660222633213525491153993788603133614823603308092263670307429249398052831768852287399239278361307882890742227030045015179537285828942317758313850019192518407369927068430051994277139965802421746868129950797361901106186970024775796489513905851973339847157762501308580800502495027392958090518895906759256028195554314827092856893603657047143804306103220853543636807760756534180130509125170115504065324353561084551767456467878703283665422060927522071396168475416128694559793418710960672785008898349443416966186272115015528492165962940991729769340824231426876504867920577869281501901804096730292773144432424887462051156785427644205604215374952018703981575182328924870014307150085493945632829675123006595247234532574938060508776215235370066650382105593746728547998743762431517604773702760233101859929511114212932267857765990857382140489234741947866140907980598108664549673727187074711239836689116097288620581358830303241790836444847681194821509578811459678263600516453222598318037477754126391457584534319712461178769585092647520675576647939421432808737830198555326796245245489758174268067138918937781344872108036430889485989461562619953240046062044177687824964232124786265135917925812192483511881913668562654848728059461911574833374044736015633178630003140593921205988065743099417245350176222214467669330355585022856544648776913145130334647730048504728338625815682032313221900408277209756778448546602924241895522908887880797012946226052971350804340998708866943504204906305614684021356038664200718847053076037268381198311058380151446417978155424503611683009386886275604564329832152702655546637819729908922776285026346093450116899884844889555780437589419688034337160205185469518791220295215828593362878179851345221062916564888159960917053424992148515196985029835642251456886624559444463830826674111037442858638378057717137174163380674878738179153435460794919216945248979306975608053878633492689395261192727780298007467634434867571622989147503227832641239487734235963289946609903339498202882367309906829047004222354049621383955054611438740970792476532784310988589175419618243361133405450675227693059287434134766374707750287887776110548906026450779914157099487036326203021949261960428516592804550371636947342708587779600097707366437519628712007537425410894371357783438601388840422933314722406392853404054855707157064591548312803154552116411348012701957636877551732560979865303416268276511847018180549254981330913912831070942527131241930418396901280664410091775133475241651254492794081725232927382489444114875946540112363471403147573018808668039222528527061450954391597166486373311930767351781414663084063230624280280559723627734933873050214607251282409184492445126845098928708517988624070907631643228530550999755731583906200928219981156436472764071605541403496527898942666713193984017866489862860732107338521129217992113619708971629968245105907806120668597550336741459329308720382454548626862546672715217922322643682171895173954007746798338974770562166311895871863768014795686917681543776389712810133649719091321492131067452978329901943678682346372614021007083784066720173081620546463342289841923439299298600690930662665317374463481871793977038768887182887252678228705028439822730920891928673622500610671040234497679450047108908818089820986146491258680252643333217015039955333775342848169731653697176955019715950727570925079387235230484698328506124158146351676728199043863628432843633318211955194193390794570262065114980633004152563073594584220260320340579963010782705796140559025717974665875702271696269672331367554175245140803294134068464947482290539833199567295948633841644275395191401751753498272673343336706563841295320515057403077782042781868304428237428900443172697770178315943748473322399413755801374882227727954775447534633771853299368391666957462400111665561642879575670865757057612450710123181072687301531911923788254178734689604634120808179502390340928917890916704470112014516523013574344837212548417489618592316013539449349199148550092473043235509648602435705063335310744320759325819171581114561887147991764664828837631294273650417001081760128415395889311512021495620616254318316641658233590396761698712356492305544893045329238929406427748892068255574554210140628816694001465610496562794430680113061381163415570366751579020832606343999720836095892801060822835607355968873224692047318281746170220190529364553163275988414697979551244024147677705272708238824719963708692466064137906968628956275953519209966151376627002128624768817391911225878493910737341661723139198101685452071047213595282130020588337927905921764315873957497295599678961510276721219946260948459364204208395854416024008095753219108769236137767386676902676483930627769829361063614474648427958264996335973758593013923299717346547091461074083121052447918484140000697909760267997347942910981610077816938269881704295634574449523676588617091810028963255051121889939630805736818229402938200090728268834839655232578427609310116201975084621558432494678438077956520221935303765223156645845692152004745786369822381966011794674948529155180235195589210315106256761000802596224308196950134347628851589489479010363959939979760616952228076909655581533307743308790173430575426597340963813378930104337509160065603517465191750706633632271347314792197368880203789649998255225599330006630142722545974805457654325295739260913563876190808528457270474927591862372195275150922985657954426492654499773179327912900861918553930976724709495062288446103918763303904805108699445161740586942108385385769619988135534075444045084970513312628677112049412011026974212234358097497993509439229507624664130927871026276302474090100150050598457619429807725861046166730641728024566423561433506647590466552674739156227099835991206337020623233415919321631713019506577799490525875004361936001674983424643193635062986355864186760651847716090309522978678856823812681020344069511812122692535855113933768363750567051680217747845203615172558188226262344278884740203091740237987228251387095648532644729036535575950029661164811389887287573716718428307219876469972432564469414104756255016226401926230938339672680322434309243814774749624873503855951425480685347384583173395679938583941096416233381023833618313152109432250410021984157448441916460201695920717451233555501273685312489095159995812541438392015912342534110339533098370380709774226192553302857940468297449139826220469693268660362215165579090623582370799455630386990962068604529434344139302788149492270649405031929371532260878668388177408661060124925847087971525281781065708203929231950308825068918588826464738109362459433995184422654150818299193914226890463063125937816240360121436298286631538542066510800153540147258959416547440415954217119726419373974945039606378895208849495760198206371916111246815786718777262100010468646404019960219143664724151167254074048225564434518616742855148829256377150434448825766828349094462086052273441044073001360924032522594828488676414139651743029626269323376487420176571169347803329029556478347349687685382280071186795547335729490176920124227937327703527933838154726593851415012038943364622954252015214432773842342185155459399099696409254283421153644833722999616149631852601458631398960114457200683951565062637400984052761977876260599504484070209721882960533203056844749973828383989950099452140838189622081864814879436088913703458142862127926859057123913877935582929127263844784869316397389817496597689918693512928778308964650870642425934326691558781449558572076630491677426108804131625780786544299822033011131660676274557699689430156680741180165404613183515371462469902641588442614369961963918065394144537111351502250758976864291447115887915692500959625920368496353421502599713856998290121087343406497539868095055309348501238789824475695292598666992357888125065429040025124751369647904525944795337962801409777715741354642844680182852357190215305161042677181840388037826709006525456258505775203266217678054227588372823393935164183271103046376103569808423770806434727989670935548033639250444917472170848309313605750776424608298147049586488467041211571343825243396028893464075095090204836514638657221621244373102557839271382210280210768747600935199078759116446243500715357504274697281641483756150329762361726628746903025438810761768503332519105279687336427399937188121575880238685138011655092996475555710646613392888299542869107024461737097393307045399029905433227483686359353735561991834455804864431029067941515162089541822242384059741075478940572983913180025822661129915901873887706319572879226715985623058938479254632376033778832396971071640436891509927766339812262274487908713403356945946889067243605401821544474299473078130997662002303102208884391248211606239313256795896290609624175594095683428132742436402973095578741668702236800781658931500157029696060299403287154970862267508811110723383466517779251142827232438845657256516732386502425236416931290784101615661095020413860487838922427330146212094776145444394039850647311302648567540217049935443347175210245315280734201067801933210035942352653801863419059915552919007572320898907771225180584150469344313780228216491607635132777331890986495446138814251317304672505844994242244477789021879470984401716858010259273475939561014760791429668143908992567261053145828244407998045852671249607425759849251491782112572844331227972223191541333705551872142931918902885856858708169033743936908957671773039745960847262448965348780402693931674634469763059636389014900373381721743378581149457375161391632061974386711798164497330495166974910144118365495341452350211117702481069197752730571937048539623826639215549429458770980912168056670272533761384652964371706738318735387514394388805527445301322538995707854974351816310151097463098021425829640227518581847367135429388980004885368321875981435600376871270544718567889171930069442021146665736120319642670202742785357853229577415640157727605820567400635097881843877586628048993265170813413825592350909027462749066545695641553547126356562096520919845064033220504588756673762082562724639704086261646369124472205743797327005618173570157378650940433401961126426353072547719579858324318665596538367589070733154203161531214014027986181386746693652510730362564120459224622256342254946435425899431203545381582161426527549987786579195310046410999057821823638203580277070174826394947133335659699200893324493143036605366926056460899605680985448581498412255295390306033429877516837072966465436019122727431343127333635760896116132184108594758697700387339916948738528108315594793593188400739784345884077188819485640506682485954566074606553372648916495097183934117318630701050354189203336008654081027323167114492096171964964930034546533133265868723174093589698851938444359144362633911435251421991136546044596433681125030533552011724883972502355445440904491049307324562934012632166660850751997766688767142408486582684858847750985797536378546253969361761524234916425306207907317583836409952193181421642181665910597759709669539728513103255749031650207628153679729211013016017028998150539135289807027951285898733293785113584813483616568377708762257040164706703423247374114526991659978364797431692082213769759570087587674913633667166835328192064766025752870153889102139093415221411871445022158634888508915797187423666119970687790068744111386397738772376731688592664968419583347873120005583278082143978783543287852880622535506159053634365076595596189412708936734480231706040408975119517046445894545835223505600725826150678717241860627420874480929615800676972467459957427504623652161775482430121785253166765537216037966290958579055728094357399588233241441881564713682520850054088006420769794465575601074781030812715915832082911679519838084935617824615277244652266461946470321387444603412778727710507031440834700073280524828139721534005653069058170778518337578951041630317199986041804794640053041141780367798443661234602365914087308511009526468227658163799420734898977562201207383885263635411941235998185434623303206895348431447813797675960498307568831350106431238440869595561293924695536867083086156959905084272603552360679764106501029416896395296088215793697874864779983948075513836060997313047422968210210419792720801200404787660955438461806888369333845133824196531388491468053180723732421397913249816798687929650696164985867327354573053704156052622395924207000034895488013399867397145549080503890846913494085214781728722476183829430854590501448162752556094496981540286840911470146910004536413441741982761628921380465505810098754231077921624733921903897826011096765188261157832292284607600237289318491119098300589733747426457759011759779460515755312838050040129811215409847506717381442579474473950518197996998988030847611403845482779076665387165439508671528771329867048190668946505216875458003280175873259587535331681613567365739609868444010189482499912761279966500331507136127298740272882716264786963045678193809540426422863523746379593118609763757546149282897721324632724988658966395645043095927696548836235474753114422305195938165195240255434972258087029347105419269288480999406776703772202254248525665631433855602470600551348710611717904874899675471961475381233206546393551313815123704505007502529922880971490386293052308336532086401228321178071675332379523327633736957811354991799560316851031161670795966081585650975328889974526293750218096800083749171232159681753149317793209338032592385804515476148933942841190634051017203475590606134626792755696688418187528352584010887392260180758627909411313117213944237010154587011899361412569354782426632236451826778797501483058240569494364378685835921415360993823498621628223470705237812750811320096311546916983634016121715462190738737481243675192797571274034267369229158669783996929197054820811669051191680915657605471612520501099207872422095823010084796035872561677775063684265624454757999790627071919600795617126705516976654918519035488711309627665142897023414872456991311023484663433018110758278954531179118539972781519349548103430226471717206965139407474613532470251596468576613043933419408870433053006246292354398576264089053285410196461597515441253445929441323236905468122971699759221132707540914959695711344523153156296890812018006071814914331576927103325540007677007362947970827372020797710855986320968698747251980318944760442474788009910318595805562340789335938863105000523432320200998010957183236207558362703702411278221725930837142757441462818857521722441288341417454723104302613672052203650068046201626129741424433820706982587151481313466168824371008828558467390166451477823917367484384269114003559339777366786474508846006211396866385176396691907736329692570750601947168231147712600760721638692117109257772969954984820462714171057682241686149980807481592630072931569948005722860034197578253131870049202638098893813029975224203510486094148026660152842237498691419199497504972607041909481104093240743971804445685172907143106396342952856195693896779146456363192239243465819869490874829884495934675646438915448232543532121296716334577939072477928603831524583871305440206581289039327214991101650556583033813727884984471507834037059008270230659175768573123495132079422130718498098195903269707226855567575112537948843214572355794395784625047981296018424817671075129985692849914506054367170324876993404752765467425061939491223784764629933349617894406253271452001256237568482395226297239766898140070488885787067732142234009142617859510765258052133859092019401891335450326272812925288760163310883902711379418641169696758209163555152318805178490421188540321736399483546777401681962522245873608542415465680287538821230414907352479324423352060578567191262169801444673203754754510241825731932861081062218655127891963569110514010538437380046759953937955822312175035767875213734864082074187807516488118086331437345151271940538088425166625955263984366821369996859406078794011934256900582754649823777785532330669644414977143455351223086854869665352269951495271661374184317967686778099591722790243221551453397075758104477091112119202987053773947028649195659001291133056495795093694385315978643961335799281152946923962731618801688941619848553582021844575496388316990613113724395435670167847297344453362180270091077223714973653906549883100115155110444219562410580311965662839794814530481208779704784171406637121820148654778937083435111840039082946575007851484803014970164357748543113375440555536169173325888962557141361621942282862825836619325121261820846564539205080783054751020693024391946121366507310604738807272219701992532365565132428377010852496772167358760512265764036710053390096660501797117632690093170952995777645950378616044945388561259029207523467215689011410824580381756638866594549324772306940712565865233625292249712112223889451093973549220085842900512963673796978050738039571483407195449628363052657291412220399902292633562480371287992462574589105628642216561398611159577066685277593607146595945144292842935408451687196845447883588651987298042363122448267439020134696583731723488152981819450745018669086087168929057472868758069581603098719335589908224866524758348745507205918274767072617510555885124053459887636528596852426981191331960777471472938549045608402833513626688069232648218585336915936769375719719440276372265066126949785392748717590815507554873154901071291482011375929092368356771469449000244268416093799071780018843563527235928394458596503472101057333286806015982133510137139267892661478870782007886380291028370031754894092193879331402449663258540670691279617545451373137453327284782077677356317828104826045992253201661025229437833688104128136231985204313082318456223610287189866350280908678507868932547021670098056321317653627385978992916215933279826918379453536657710158076560700701399309069337334682625536518128206022961231112817112747321771294971560177269079108071326377499389328959765502320549952891091181910179013853508741319747356666782984960044666224657151830268346302823044980284049272429074920612764769515301671493875841853648323271800956136371567156366681788044805806609205429737934885019366995847436926405415779739679659420036989217294203859440974282025334124297728303730327668632445824754859196705865931535052517709460166800432704051366158355724604808598248246501727326656663293436158704679484942596922217957218131695571762571099556827302229821684056251526677600586244198625117772272045224552465366228146700631608333042537599888334438357120424329134242942387549289876818927312698468088076211745821265310395365879191820497609659071082109083295529887985483476986425655162787451582510381407683986460550650800851449907526956764490351397564294936664689255679240674180828418885438112852008235335171162368705726349582998918239871584604110688487978504379383745681683358341766409603238301287643507694455106954670761070593572251107931744425445789859371183305998534389503437205569319886938618836584429633248420979167393656000279163904107198939177164392644031126775307952681718253829779809470635446836724011585302020448755975852322294727291761175280036291307533935862093031371043724046480790033848623372997871375231182608088774121506089262658338276860801898314547928952786404717869979411662072094078235684126042502704400321038489723278780053739051540635795791604145583975991904246780891230763862232613323097323516069372230170638936385525351572041735003664026241406986076700282653452908538925916878947552081515859999302090239732002652057089018389922183061730118295704365425550476323411382908189971036744948878110060369194263181770597061799909271731165160344767421572390689883798024915378441567505321561922043479778064696234776843354154307847995254213630177/0.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793348766303427248602563378691208853255039241149568065044322737281915193947264411947377336118796228332674609000056462085709446106939190333690926542826492010614872113375868104567782733894190051380497995595957314663203658743153972107729659533623172039975156682287843712946756253175992321156343515329456270114)
1⅄2Θn23=(1Θn24/1Θn23)=(28657/46368)/(17711/28657)=(0.61803398895790200138026224982746721877156659765355417529330572808833678/0.618033988205325051470844819764804410789684893743238999197403775691803049865652371148410510520989636040060020239383047771923090344418466692256691209826569424573402659036186621069895662490839934396482534808249293366367728652685207802631119796210350001744774400669993369857277454025194542345674704260739086436123809191471542729525072408137627804724849077014342045573507345500226820672087099138081446069023275290504937711553896081236696095194891300554838259413057891614614230380011864465924555954915029486687371322887950587988973025787765641902502006490560770492375335869072128973723697525909899849949401542380570192274138953833269358271975433576438566493352409533447325260843772900164008793662979376766584080678368286980493422200509474124995638063998325016575356806364937013644135813239348152283909690477021321143176187318979655930488187877307464144886066231636249432948319782252154796384827441811773737655721115259796908259762012771748612904351467355270963464424049970338835188610112712426283281571692780123530027567435530585895243744983773598073769061660327319677565690756185225250375126496144048574519314652615416826604320061416058903583766618976166381686847890567749589978015842551558083539798304079282548766444498726314687510904840004187458561607984087657465889660466901629619290225773807446697142059531702550860173779530306731339637784834420909376417629200544369613009037931395470565655860697211850507729350594968070628467739121331611822591338939875074152912028474718218934291796070768049691174931081411173535261890637540566004815577345849181700806085773109536936874062183759639878563701713368461457933489199846459852741040583452559584045782880273580626025054960393621104791150504239801793628083888753184213281222737899989531353595980039780856335275848832745925951774435565481383257144851170743622849565551174233171650905537913947726558955926998639075967477405171511323585860348256970373730676623512579823428830652196670970443521652650312314617719928813204452664270509823079875772062672296472066161845273406148584987961056635377045747984785567226157657814844540600900303590745716578846355166277000383850368147398541368601039885542799316048434937362599015947238022123739400495515929790278117039466796943155250026171616010049900547859161810377918135185120563911086296541857137872073140942876086122064417070872736155215130683602610182503402310081306487071221691035349129357574065673308441218550441427923369508322573891195868374219213455700177966988868339323725442300310569843319258819834595386816484628537530097358411557385630038036081934605855462888648497749241023135708552884112084307499040374079631503646578497400286143001709878912656593502460131904944690651498761210175524304707401333007642111874934570959974875248630352095474055204662037198590222284258645357155319817147642809784694838957322818159611962173290993474543741494224796733782321945772411627176606064835816728896953623896430191576229193565272010329064451966360749555082527829151690686394249223575391701852950413511532958788428656174756603971106535924904909795163485361342778378755626897442160728617789719789231252399064800921240883553756499284642495725302718358516243849670237638273371253096974561189238231496667480894720312663572600062811878424119761314861988344907003524444289353386607111700457130892975538262902606692954600970094566772516313640646264438008165544195135568970932058484837910458177757615940258924521059427016086819974177338870084098126112293680427120773284014376941061520745367623966221167603028928359563108490072233660187737725512091286596643054053110932756394598178455525700526921869002337997696897791115608751788393760686743204103709390375824405904316571867257563597026904421258331297763199218341068499842970303939700596712845029137732491188889276616533482220748857172767561154342743483267613497574763583068709215898384338904979586139512161077572669853787905223854555605960149352688697351432459782950064556652824789754684719265798932198066789964057647346198136580940084447080992427679101092228774819415849530655686219771783508392364867222668109013504553861185748682695327494155005757755522210978120529015598283141989740726524060438985239208570331856091007432738946854171755592001954147328750392574240150748508217887427155668772027776808458666294448127857068081097114143141291830966256063091042328226960254039152737551034651219597306068325365530236940363610985099626618278256621418850542624838608367938025613288201835502669504833025089855881634504658547649788882297518930802247269428062951460376173360784450570541229019087831943329727466238615347035628293261681264612485605611194472554698677461004292145025648183689848902536901978574170359772481418152632864570611019995114631678124018564399623128729455281432110828069930557978853334263879680357329797257214642146770422584359842272394179432599364902118156122413371951006734829186586174407649090972537250933454304358446452873643437903479080154935966779495411243326237917437275360295913738353630875527794256202672994381826429842621349059566598038873573646927452280420141675681334403461632410929266845796838468785985972013818613253306347489269637435879540775377743657745053564574100568796454618417838573472450012213420804689953589000942178176361796419722929825173605052866664340300799106675506856963394633073943539100394319014551418501587744704609693966570122483162927033534563980877272568656872666364239103883867815891405241302299612660083051261471891684405206406811599260215654115922811180514359493317514045433925393446627351083504902816065882681369298949645810796663991345918972676832885507903828035035069965453466866734131276825906410301148061555640855637366088564748578008863453955403566318874969466447988275116027497644554559095508950692675437065987367833339149248002233311232857591513417315141152249014202463621453746030638238475765083574693792092682416163590047806818578357818334089402240290330460271486896744250968349792371846320270788986983982971001849460864710192972048714101266706214886415186516383431622291237742959835293296576752625885473008340021635202568307917786230240429912412325086366332833164671807935233974247129846110897860906584778588128554977841365111491084202812576333880029312209931255888613602261227623268311407335031580416652126879994416721917856021216456712147119377464493840946365634923404403810587291063265519768293959591024880482953554105454164776494399274173849321282758139372579125519070384199323027532540042572495376347838224517569878214746833234462783962033709041420944271905642600411766758558118435286317479149945911993579230205534424398925218969187284084167917088320480161915064382175384722755347733538053529678612555396587221272289492968559165299926719475171860278465994346930941829221481662421048958369682800013958195205359946958858219632201556338765397634085912691488990473531772341836200579265101022437798792616114736364588058764001814565376696793104651568552186202324039501692431168649893568761559130404438706075304463132916913843040094915727396447639320235893498970583103604703911784206302125135220016051924486163939002686952577031789789580207279198799595212339044561538193111630666154866175803468611508531946819276267578602086750183201312070349303835014132672645426946295843947377604075792999965104511986600132602854450919496109153086505914785218271277523816170569145409498551837247443905503018459713159088529853089995463586558258017238371078619534494189901245768922078375266078096102173988903234811738842167707715392399762710681508880901699410266252573542240988240220539484244687161949959870188784590152493282618557420525526049481802003001011969152388596154517220923334612834560491328471228670132951809331053494783124541996719824126740412464668318386432634260390131555989810517500087238720033499668492863872701259727117283735213036954321806190459573577136476253620406881390236242453850717102278675367275011341033604354956904072303451163764525246885577694804061834804759744565027741912970652894580730711519000593223296227797745751474334368566144397529399448651289388282095125100324528038524618766793453606448686184876295494992497470077119028509613706947691663467913598771678821928324667620476672366263042188645008200439683148968838329204033918414349024671110025473706249781903199916250828767840318246850682206790661967407614195484523851066057158809365948982796524409393865373207244303311581812471647415989112607739819241372090588686882786055762989845412988100638587430645217573367763548173221202498516941759430505635621314164078584639006176501378371776529294762187249188679903688453083016365983878284537809261262518756324807202428725965732630770841330216003070802945179188330948808319084342394528387479498900792127577904176989915203964127438322224936315734375545242000209372928080399204382873294483023345081480964511288690372334857102976585127543008688976515336566981889241721045468820881460027218480650451896569773528282793034860592525386467529748403531423386956066580591129566946993753707645601423735910946714589803538402484558746554070558676763094531877028300240778867292459085040304288655476846843703109187981993928185085668423072896674459992322992637052029172627979202289144013679031301252748019681055239557525211990089681404194437659210664061136894999476567679799001989042816763792441637296297588721778274069162857242558537181142478277558711658582545276895697386327947796349931953798373870258575566179293017412848518686533831175628991171441532609833548522176082632515615730885996440660222633213525491153993788603133614823603308092263670307429249398052831768852287399239278361307882890742227030045015179537285828942317758313850019192518407369927068430051994277139965802421746868129950797361901106186970024775796489513905851973339847157762501308580800502495027392958090518895906759256028195554314827092856893603657047143804306103220853543636807760756534180130509125170115504065324353561084551767456467878703283665422060927522071396168475416128694559793418710960672785008898349443416966186272115015528492165962940991729769340824231426876504867920577869281501901804096730292773144432424887462051156785427644205604215374952018703981575182328924870014307150085493945632829675123006595247234532574938060508776215235370066650382105593746728547998743762431517604773702760233101859929511114212932267857765990857382140489234741947866140907980598108664549673727187074711239836689116097288620581358830303241790836444847681194821509578811459678263600516453222598318037477754126391457584534319712461178769585092647520675576647939421432808737830198555326796245245489758174268067138918937781344872108036430889485989461562619953240046062044177687824964232124786265135917925812192483511881913668562654848728059461911574833374044736015633178630003140593921205988065743099417245350176222214467669330355585022856544648776913145130334647730048504728338625815682032313221900408277209756778448546602924241895522908887880797012946226052971350804340998708866943504204906305614684021356038664200718847053076037268381198311058380151446417978155424503611683009386886275604564329832152702655546637819729908922776285026346093450116899884844889555780437589419688034337160205185469518791220295215828593362878179851345221062916564888159960917053424992148515196985029835642251456886624559444463830826674111037442858638378057717137174163380674878738179153435460794919216945248979306975608053878633492689395261192727780298007467634434867571622989147503227832641239487734235963289946609903339498202882367309906829047004222354049621383955054611438740970792476532784310988589175419618243361133405450675227693059287434134766374707750287887776110548906026450779914157099487036326203021949261960428516592804550371636947342708587779600097707366437519628712007537425410894371357783438601388840422933314722406392853404054855707157064591548312803154552116411348012701957636877551732560979865303416268276511847018180549254981330913912831070942527131241930418396901280664410091775133475241651254492794081725232927382489444114875946540112363471403147573018808668039222528527061450954391597166486373311930767351781414663084063230624280280559723627734933873050214607251282409184492445126845098928708517988624070907631643228530550999755731583906200928219981156436472764071605541403496527898942666713193984017866489862860732107338521129217992113619708971629968245105907806120668597550336741459329308720382454548626862546672715217922322643682171895173954007746798338974770562166311895871863768014795686917681543776389712810133649719091321492131067452978329901943678682346372614021007083784066720173081620546463342289841923439299298600690930662665317374463481871793977038768887182887252678228705028439822730920891928673622500610671040234497679450047108908818089820986146491258680252643333217015039955333775342848169731653697176955019715950727570925079387235230484698328506124158146351676728199043863628432843633318211955194193390794570262065114980633004152563073594584220260320340579963010782705796140559025717974665875702271696269672331367554175245140803294134068464947482290539833199567295948633841644275395191401751753498272673343336706563841295320515057403077782042781868304428237428900443172697770178315943748473322399413755801374882227727954775447534633771853299368391666957462400111665561642879575670865757057612450710123181072687301531911923788254178734689604634120808179502390340928917890916704470112014516523013574344837212548417489618592316013539449349199148550092473043235509648602435705063335310744320759325819171581114561887147991764664828837631294273650417001081760128415395889311512021495620616254318316641658233590396761698712356492305544893045329238929406427748892068255574554210140628816694001465610496562794430680113061381163415570366751579020832606343999720836095892801060822835607355968873224692047318281746170220190529364553163275988414697979551244024147677705272708238824719963708692466064137906968628956275953519209966151376627002128624768817391911225878493910737341661723139198101685452071047213595282130020588337927905921764315873957497295599678961510276721219946260948459364204208395854416024008095753219108769236137767386676902676483930627769829361063614474648427958264996335973758593013923299717346547091461074083121052447918484140000697909760267997347942910981610077816938269881704295634574449523676588617091810028963255051121889939630805736818229402938200090728268834839655232578427609310116201975084621558432494678438077956520221935303765223156645845692152004745786369822381966011794674948529155180235195589210315106256761000802596224308196950134347628851589489479010363959939979760616952228076909655581533307743308790173430575426597340963813378930104337509160065603517465191750706633632271347314792197368880203789649998255225599330006630142722545974805457654325295739260913563876190808528457270474927591862372195275150922985657954426492654499773179327912900861918553930976724709495062288446103918763303904805108699445161740586942108385385769619988135534075444045084970513312628677112049412011026974212234358097497993509439229507624664130927871026276302474090100150050598457619429807725861046166730641728024566423561433506647590466552674739156227099835991206337020623233415919321631713019506577799490525875004361936001674983424643193635062986355864186760651847716090309522978678856823812681020344069511812122692535855113933768363750567051680217747845203615172558188226262344278884740203091740237987228251387095648532644729036535575950029661164811389887287573716718428307219876469972432564469414104756255016226401926230938339672680322434309243814774749624873503855951425480685347384583173395679938583941096416233381023833618313152109432250410021984157448441916460201695920717451233555501273685312489095159995812541438392015912342534110339533098370380709774226192553302857940468297449139826220469693268660362215165579090623582370799455630386990962068604529434344139302788149492270649405031929371532260878668388177408661060124925847087971525281781065708203929231950308825068918588826464738109362459433995184422654150818299193914226890463063125937816240360121436298286631538542066510800153540147258959416547440415954217119726419373974945039606378895208849495760198206371916111246815786718777262100010468646404019960219143664724151167254074048225564434518616742855148829256377150434448825766828349094462086052273441044073001360924032522594828488676414139651743029626269323376487420176571169347803329029556478347349687685382280071186795547335729490176920124227937327703527933838154726593851415012038943364622954252015214432773842342185155459399099696409254283421153644833722999616149631852601458631398960114457200683951565062637400984052761977876260599504484070209721882960533203056844749973828383989950099452140838189622081864814879436088913703458142862127926859057123913877935582929127263844784869316397389817496597689918693512928778308964650870642425934326691558781449558572076630491677426108804131625780786544299822033011131660676274557699689430156680741180165404613183515371462469902641588442614369961963918065394144537111351502250758976864291447115887915692500959625920368496353421502599713856998290121087343406497539868095055309348501238789824475695292598666992357888125065429040025124751369647904525944795337962801409777715741354642844680182852357190215305161042677181840388037826709006525456258505775203266217678054227588372823393935164183271103046376103569808423770806434727989670935548033639250444917472170848309313605750776424608298147049586488467041211571343825243396028893464075095090204836514638657221621244373102557839271382210280210768747600935199078759116446243500715357504274697281641483756150329762361726628746903025438810761768503332519105279687336427399937188121575880238685138011655092996475555710646613392888299542869107024461737097393307045399029905433227483686359353735561991834455804864431029067941515162089541822242384059741075478940572983913180025822661129915901873887706319572879226715985623058938479254632376033778832396971071640436891509927766339812262274487908713403356945946889067243605401821544474299473078130997662002303102208884391248211606239313256795896290609624175594095683428132742436402973095578741668702236800781658931500157029696060299403287154970862267508811110723383466517779251142827232438845657256516732386502425236416931290784101615661095020413860487838922427330146212094776145444394039850647311302648567540217049935443347175210245315280734201067801933210035942352653801863419059915552919007572320898907771225180584150469344313780228216491607635132777331890986495446138814251317304672505844994242244477789021879470984401716858010259273475939561014760791429668143908992567261053145828244407998045852671249607425759849251491782112572844331227972223191541333705551872142931918902885856858708169033743936908957671773039745960847262448965348780402693931674634469763059636389014900373381721743378581149457375161391632061974386711798164497330495166974910144118365495341452350211117702481069197752730571937048539623826639215549429458770980912168056670272533761384652964371706738318735387514394388805527445301322538995707854974351816310151097463098021425829640227518581847367135429388980004885368321875981435600376871270544718567889171930069442021146665736120319642670202742785357853229577415640157727605820567400635097881843877586628048993265170813413825592350909027462749066545695641553547126356562096520919845064033220504588756673762082562724639704086261646369124472205743797327005618173570157378650940433401961126426353072547719579858324318665596538367589070733154203161531214014027986181386746693652510730362564120459224622256342254946435425899431203545381582161426527549987786579195310046410999057821823638203580277070174826394947133335659699200893324493143036605366926056460899605680985448581498412255295390306033429877516837072966465436019122727431343127333635760896116132184108594758697700387339916948738528108315594793593188400739784345884077188819485640506682485954566074606553372648916495097183934117318630701050354189203336008654081027323167114492096171964964930034546533133265868723174093589698851938444359144362633911435251421991136546044596433681125030533552011724883972502355445440904491049307324562934012632166660850751997766688767142408486582684858847750985797536378546253969361761524234916425306207907317583836409952193181421642181665910597759709669539728513103255749031650207628153679729211013016017028998150539135289807027951285898733293785113584813483616568377708762257040164706703423247374114526991659978364797431692082213769759570087587674913633667166835328192064766025752870153889102139093415221411871445022158634888508915797187423666119970687790068744111386397738772376731688592664968419583347873120005583278082143978783543287852880622535506159053634365076595596189412708936734480231706040408975119517046445894545835223505600725826150678717241860627420874480929615800676972467459957427504623652161775482430121785253166765537216037966290958579055728094357399588233241441881564713682520850054088006420769794465575601074781030812715915832082911679519838084935617824615277244652266461946470321387444603412778727710507031440834700073280524828139721534005653069058170778518337578951041630317199986041804794640053041141780367798443661234602365914087308511009526468227658163799420734898977562201207383885263635411941235998185434623303206895348431447813797675960498307568831350106431238440869595561293924695536867083086156959905084272603552360679764106501029416896395296088215793697874864779983948075513836060997313047422968210210419792720801200404787660955438461806888369333845133824196531388491468053180723732421397913249816798687929650696164985867327354573053704156052622395924207000034895488013399867397145549080503890846913494085214781728722476183829430854590501448162752556094496981540286840911470146910004536413441741982761628921380465505810098754231077921624733921903897826011096765188261157832292284607600237289318491119098300589733747426457759011759779460515755312838050040129811215409847506717381442579474473950518197996998988030847611403845482779076665387165439508671528771329867048190668946505216875458003280175873259587535331681613567365739609868444010189482499912761279966500331507136127298740272882716264786963045678193809540426422863523746379593118609763757546149282897721324632724988658966395645043095927696548836235474753114422305195938165195240255434972258087029347105419269288480999406776703772202254248525665631433855602470600551348710611717904874899675471961475381233206546393551313815123704505007502529922880971490386293052308336532086401228321178071675332379523327633736957811354991799560316851031161670795966081585650975328889974526293750218096800083749171232159681753149317793209338032592385804515476148933942841190634051017203475590606134626792755696688418187528352584010887392260180758627909411313117213944237010154587011899361412569354782426632236451826778797501483058240569494364378685835921415360993823498621628223470705237812750811320096311546916983634016121715462190738737481243675192797571274034267369229158669783996929197054820811669051191680915657605471612520501099207872422095823010084796035872561677775063684265624454757999790627071919600795617126705516976654918519035488711309627665142897023414872456991311023484663433018110758278954531179118539972781519349548103430226471717206965139407474613532470251596468576613043933419408870433053006246292354398576264089053285410196461597515441253445929441323236905468122971699759221132707540914959695711344523153156296890812018006071814914331576927103325540007677007362947970827372020797710855986320968698747251980318944760442474788009910318595805562340789335938863105000523432320200998010957183236207558362703702411278221725930837142757441462818857521722441288341417454723104302613672052203650068046201626129741424433820706982587151481313466168824371008828558467390166451477823917367484384269114003559339777366786474508846006211396866385176396691907736329692570750601947168231147712600760721638692117109257772969954984820462714171057682241686149980807481592630072931569948005722860034197578253131870049202638098893813029975224203510486094148026660152842237498691419199497504972607041909481104093240743971804445685172907143106396342952856195693896779146456363192239243465819869490874829884495934675646438915448232543532121296716334577939072477928603831524583871305440206581289039327214991101650556583033813727884984471507834037059008270230659175768573123495132079422130718498098195903269707226855567575112537948843214572355794395784625047981296018424817671075129985692849914506054367170324876993404752765467425061939491223784764629933349617894406253271452001256237568482395226297239766898140070488885787067732142234009142617859510765258052133859092019401891335450326272812925288760163310883902711379418641169696758209163555152318805178490421188540321736399483546777401681962522245873608542415465680287538821230414907352479324423352060578567191262169801444673203754754510241825731932861081062218655127891963569110514010538437380046759953937955822312175035767875213734864082074187807516488118086331437345151271940538088425166625955263984366821369996859406078794011934256900582754649823777785532330669644414977143455351223086854869665352269951495271661374184317967686778099591722790243221551453397075758104477091112119202987053773947028649195659001291133056495795093694385315978643961335799281152946923962731618801688941619848553582021844575496388316990613113724395435670167847297344453362180270091077223714973653906549883100115155110444219562410580311965662839794814530481208779704784171406637121820148654778937083435111840039082946575007851484803014970164357748543113375440555536169173325888962557141361621942282862825836619325121261820846564539205080783054751020693024391946121366507310604738807272219701992532365565132428377010852496772167358760512265764036710053390096660501797117632690093170952995777645950378616044945388561259029207523467215689011410824580381756638866594549324772306940712565865233625292249712112223889451093973549220085842900512963673796978050738039571483407195449628363052657291412220399902292633562480371287992462574589105628642216561398611159577066685277593607146595945144292842935408451687196845447883588651987298042363122448267439020134696583731723488152981819450745018669086087168929057472868758069581603098719335589908224866524758348745507205918274767072617510555885124053459887636528596852426981191331960777471472938549045608402833513626688069232648218585336915936769375719719440276372265066126949785392748717590815507554873154901071291482011375929092368356771469449000244268416093799071780018843563527235928394458596503472101057333286806015982133510137139267892661478870782007886380291028370031754894092193879331402449663258540670691279617545451373137453327284782077677356317828104826045992253201661025229437833688104128136231985204313082318456223610287189866350280908678507868932547021670098056321317653627385978992916215933279826918379453536657710158076560700701399309069337334682625536518128206022961231112817112747321771294971560177269079108071326377499389328959765502320549952891091181910179013853508741319747356666782984960044666224657151830268346302823044980284049272429074920612764769515301671493875841853648323271800956136371567156366681788044805806609205429737934885019366995847436926405415779739679659420036989217294203859440974282025334124297728303730327668632445824754859196705865931535052517709460166800432704051366158355724604808598248246501727326656663293436158704679484942596922217957218131695571762571099556827302229821684056251526677600586244198625117772272045224552465366228146700631608333042537599888334438357120424329134242942387549289876818927312698468088076211745821265310395365879191820497609659071082109083295529887985483476986425655162787451582510381407683986460550650800851449907526956764490351397564294936664689255679240674180828418885438112852008235335171162368705726349582998918239871584604110688487978504379383745681683358341766409603238301287643507694455106954670761070593572251107931744425445789859371183305998534389503437205569319886938618836584429633248420979167393656000279163904107198939177164392644031126775307952681718253829779809470635446836724011585302020448755975852322294727291761175280036291307533935862093031371043724046480790033848623372997871375231182608088774121506089262658338276860801898314547928952786404717869979411662072094078235684126042502704400321038489723278780053739051540635795791604145583975991904246780891230763862232613323097323516069372230170638936385525351572041735003664026241406986076700282653452908538925916878947552081515859999302090239732002652057089018389922183061730118295704365425550476323411382908189971036744948878110060369194263181770597061799909271731165160344767421572390689883798024915378441567505321561922043479778064696234776843354154307847995254213630177)
1⅄2Θn24=(1Θn25/1Θn24)=(46368/75025)/(28657/46368)=(0.61803398867044318560479840053315561479506831056314561812729090303232255914695101632789070309896701099633455514828390536487837387537487504165278240586471176274575141619460179940019993335554815061646117960679773408863712095968010663112295901366211262912362545818060646451182939020326557814061979340219926691102965678107297567477507497500833055648117294235254915028323892035988003998667110963012329223592135954681772742419193602132622459180273242252582472509163612129290236587804065311562812395868043985338220593135621459513495501499500166611129623458847050983005664778407197600799733422192602465844718427190936354548483838720426524491836054648450516494501832722425858047317560813062312562479173608797067644118627124291902699100299900033322225924691769410196601132955681439520159946684438520493168943685438187270909696767744085304898367210929690103298900366544485171609463512162612462512495834721759413528823725424858380539820059980006664445184938353882039320226591136287904031989336887704098633788737087637454181939353548817060979673442185938020659780073308897034321892702432522492502499166944351882705764745084971676107964011996001332889036987670776407864045318227257580806397867377540819726757747417527490836387870709763412195934688437187604131956014661779406864378540486504498500499833388870376541152949016994335221592802399200266577807397534155281572809063645451516161279573475508163945351549483505498167277574141952682439186937687437520826391202932355881372875708097300899700099966677774075308230589/0.61803398895790200138026224982746721877156659765355417529330572808833678)
1⅄2Θn25=(1Θn26/1Θn25)=(75025/121393)/(46368/75025)=(0.6180339887802426828565073768668704126267577207911494072969611097839249380112527081462687304869308773982025322712182745298328569192622309358859242295684265155321970789089980476633743296565699834422083645679734416317250582817790152644715922664404043066733666685887983656388753882019556317085828672163963325727183610257593106686547000238893511157974512533671628512352442068323544191180710584630085754532798431540533638677683227204204525796380351420592620661817402980402494377764780506289489509279777252395113392040727224798793999654016294185002430123647986292455083901048660136910695015363324079642153995699916799156458774393910686777656042770176204558747209476658456418409628232270394503801701910324318535665153674429332828087286746352755101200233950886789188832964009456887958943266909953621708006227706704669956257774336246735808489781124117535607489723460166566441228077401497615183742060909607638002191230136828317942550229420147784468626691819132898931569365614162266358027233860272009094428838565650408178395788884037794601006647829776016739021195620834809255887901279315940787360061947558755447183939765884359065184977717001804057894606773042926692642903627062515960557857537090277034095870437339879564719547255607819231751418945079205555509790515103836300280905818292652788875800087319697181880339064031698697618478824973433394017776972313065827518884943942401950689084214081536826670401093967526957897078085227319532427734712874712709958564332375013386274332127882167835048149399059253828474458988574300000823770728130946594943695270732249800235598428245450726153896847429423442867381150478198907680014498364815104660071009036764887596484146532337119932780308584514757852594465908248416300775168255171220745842017249759047062021698120978969133310816933431087459738205662599985172126893642961291013485126819503595759228291581886929229856746270378028387139291392419661759739029433328116118721837338232023263285362417931841209954445478734358653299613651528506586046971406918026574843689504337152883609433822378555600405295198240425724712298073200266901715914426696761757267717248935276333890751526035273862578567133195489031492754936446088324697470200093909863006927911823581260863476477226858220819981382781544240606954272486881451154514675475521652813588921931248095030191197185999192704686431672336955178634682395195769113540319458288369181089519165025989966472531365070473585791602481197433130411143970410155445536398309622465875297587175537304457423409916552025240335109932203669074823095236133879218735841440610249355399405237534289456558450652014531315644229897934806784575716886476155956274249750809354740388655029532180603494435428731475455751155338446203652599408532617201980344830426795614244643430840328519766378621502063545673968021220333956653184285749590174062754854069015511602810705724382789781947888263738436318403861837173477877637096043429192787063504485431614673004209468420749137100162282833441796479203907968334253210646412890364353793052317678943596418244874086644205184812962856177868575/0.61803398867044318560479840053315561479506831056314561812729090303232255914695101632789070309896701099633455514828390536487837387537487504165278240586471176274575141619460179940019993335554815061646117960679773408863712095968010663112295901366211262912362545818060646451182939020326557814061979340219926691102965678107297567477507497500833055648117294235254915028323892035988003998667110963012329223592135954681772742419193602132622459180273242252582472509163612129290236587804065311562812395868043985338220593135621459513495501499500166611129623458847050983005664778407197600799733422192602465844718427190936354548483838720426524491836054648450516494501832722425858047317560813062312562479173608797067644118627124291902699100299900033322225924691769410196601132955681439520159946684438520493168943685438187270909696767744085304898367210929690103298900366544485171609463512162612462512495834721759413528823725424858380539820059980006664445184938353882039320226591136287904031989336887704098633788737087637454181939353548817060979673442185938020659780073308897034321892702432522492502499166944351882705764745084971676107964011996001332889036987670776407864045318227257580806397867377540819726757747417527490836387870709763412195934688437187604131956014661779406864378540486504498500499833388870376541152949016994335221592802399200266577807397534155281572809063645451516161279573475508163945351549483505498167277574141952682439186937687437520826391202932355881372875708097300899700099966677774075308230589)
Continued base chain ratios abbreviated
1⅄2Θn26=(1Θn27/1Θn26)=(121393/196418)/(75025/121393)
1⅄2Θn27=(1Θn28/1Θn27)=(196418/317811)/(121393/196418)
1⅄2Θn28=(1Θn29/1Θn28)=(317811/514229)/(196418/317811)
1⅄2Θn29=(1Θn30/1Θn29)=(514229/832040)/(317811/514229)
1⅄2Θn30=(1Θn31/1Θn30)=(832040/1346296)/(514229/832040)
1⅄2Θn31=(1Θn32/1Θn31)=(1346296/2178309)/(832040/1346296)
1⅄2Θn32=(1Θn33/1Θn32)=(2178309/3524578)/(1346296/2178309)
1⅄2Θn33=(1Θn34/1Θn33)=(3524578/5702887)/(2178309/3524578)
1⅄2Θn34=(1Θn35/1Θn34)=(5702887/9227465)/(3524578/5702887)
1⅄2Θn35=(1Θn36/1Θn35)=(9227465/14930352)/(5702887/9227465)
1⅄2Θn36=(1Θn37/1Θn36)=(14930352/24157817)/(9227465/14930352)
1⅄2Θn37=(1Θn38/1Θn37)=(24157817/39088169)/(14930352/24157817)
1⅄2Θn38=(1Θn39/1Θn38)=(39088169/63245986)/(24157817/39088169)
1⅄2Θn39=(1Θn40/1Θn39)=(63245986/102334155)/(39088169/63245986)
1⅄2Θn40=(1Θn41/1Θn40)=(102334155/165780141)/(63245986/102334155)
1⅄2Θn41=(1Θn42/1Θn41)=(165780141/269114296)/(102334155/165780141)
1⅄2Θn42=(1Θn43/1Θn42)=(269114296/434894437)/(165780141/269114296)
1⅄2Θn43=(1Θn44/1Θn43)=(434894437/704008733)/(269114296/434894437)
1⅄2Θn44=(1Θn45/1Θn44)=(704008733/1138903170)/(434894437/704008733)
And so on for 1⅄2Θn45 1⅄2Θn46 . . . of ∈1⅄2Θ
then if ∈1⅄3Θn1 of (1⅄2Θn2/1⅄2Θn1)=(0.5/0)=0
1⅄3Θn1 of (1⅄2Θn2/1⅄2Θn1)=(0.5/0)=0
1⅄3Θn2 of (1⅄2Θn3/1⅄2Θn2)=(1.2/0.5)=2.4 if 1Θn4 of1⅄2Θn3=(1Θn4/1Θn3) is c1 for 1Θn4 of1⅄2Θn3=(1Θn4c1/1Θn3) for 1Θncn variant
1⅄3Θn3 of (1⅄2Θn4/1⅄2Θn3)=(1/1.2)=0.83
1⅄3Θn4 of (1⅄2Θn5/1⅄2Θn4)=(1.0416/1)=1.0416
1⅄3Θn5 of (1⅄2Θn6/1⅄2Θn5)=(0.9878144/1.0416)=0.948362519201228878648233486943164
1⅄3Θn6 of (1⅄2Θn7/1⅄2Θn6)=(1.00595237770/0.9878144)
And so on for ∈1⅄3Θn1 of (1⅄2Θn2/1⅄2Θn1)
while alternately ∈2⅄3Θn1 of (1⅄2Θn1/1⅄2Θn2)=(0/0.5)=0
2⅄3Θn1 of (1⅄2Θn1/1⅄2Θn2)=(0/0.5)=0
2⅄3Θn2 of (1⅄2Θn2/1⅄2Θn3)=(0.5/1.2)=0.416
2⅄3Θn3 of (1⅄2Θn3/1⅄2Θn4)=(1.2/1)=1.2
2⅄3Θn4 of (1⅄2Θn4/1⅄2Θn5)=(1/1.0416)=0.960061443932411674347158218125
2⅄3Θn5 of (1⅄2Θn5/1⅄2Θn6)=(1.0416/0.9878144)
And so on for ∈2⅄3Θn1 of (1⅄2Θn2/1⅄2Θn1)
Alternate Path of divide 2⅄ to 2Θ for 2⅄2Θ from 1Θ of 2⅄(Yn1/Yn2)
2⅄2Θn=(1Θn1/1Θn2) and of cn variable paths in previous divided by later division functions
so
2⅄2Θn1=(1Θn1/1Θn2)=(0/1)/(1/1)=(0/1)=0
2⅄2Θn2=(1Θn2/1Θn3)=(1/1)/(1/2)=(1/0.5)=2
2⅄2Θn3=(1Θn3/1Θn4)=(1/2)/(2/3)=(0.5/0.6)=0.83
2⅄2Θn4=(1Θn4/1Θn5)=(2/3)/(3/5)=(0.6/0.6)=1
2⅄2Θn5=(1Θn5/1Θn6)=(3/5)/(5/8)=(0.6/0.625)=0.96
2⅄2Θn6=(1Θn6/1Θn7)=(5/8)/(8/13)=(0.625/0.615384)=1.015626
2⅄2Θn7=(1Θn7/1Θn8)=(8/13)/(13/21)=(0.615384/0.619047)=0.994082840236686390532544378698224852071005917159763313609467455621301775147928
2⅄2Θn8=(1Θn8/1Θn9)=(13/21)/(21/34)=(0.619047/0.61764705882352941)
2⅄2Θn9=(1Θn9/1Θn10)=(21/34)/(34/55)=(0.61764705882352941/0.618)
2⅄2Θn10=(1Θn10/1Θn11)=(34/55)/(55/89)=(0.618/0.6179775280878651685393258764044943820224719101123595505)
2⅄2Θn11=(1Θn11/1Θn12)=(55/89)/(89/144)=(0.6179775280878651685393258764044943820224719101123595505/0.61805)
2⅄2Θn12=(1Θn12/1Θn13)=(89/144)/(144/233)=(0.61805/0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566)
2⅄2Θn13=(1Θn13/1Θn14)=(144/233)/(233/377)=(0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566/0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257)
2⅄2Θn14=(1Θn14/1Θn15)=(233/377)/(377/610)=(0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/0.618032786885245901639344262295081967213114754098360655737749)
2⅄2Θn15=(1Θn15/1Θn16)=(377/610)/(610/987)=(0.618032786885245901639344262295081967213114754098360655737749/0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870)
2⅄2Θn16=(1Θn16/1Θn17)=(610/987)/(987/1597)=(0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870/0.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129)
2⅄2Θn17=(1Θn17/1Θn18)=(987/1597)/(1597/2584)=(0.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/0.618034055727554179566563467492260061919504643962848297213622291021671826625386996904024767801857585139318885448916408668730650154798761609907120743)
2⅄2Θn18=(1Θn18/1Θn19)=(1597/2584)/(2584/4181)=(0.618034055727554179566563467492260061919504643962848297213622291021671826625386996904024767801857585139318885448916408668730650154798761609907120743/0.618033963166706529538387945467591485290600334848122458741927768476441042812724228653432193255202104759626883520688830423343697679980865821573786175556087060511839272901219803874671131308299449892370246352547237502989715379095910069361396795025113609184405644582635733078210954317149007414494140157856972016264051662281750777325998564936)
2⅄2Θn19=(1Θn19/1Θn20)=(2584/4181)/(4181/6765)=(0.618033963166706529538387945467591485290600334848122458741927768476441042812724228653432193255202104759626883520688830423343697679980865821573786175556087060511839272901219803874671131308299449892370246352547237502989715379095910069361396795025113609184405644582635733078210954317149007414494140157856972016264051662281750777325998564936/0.61803399852)
2⅄2Θn20=(1Θn20/1Θn21)=(4181/6765)/(6765/10946)=(0.61803399852/0.6180339850173579389731408733784030696144710396491869175954686643522748035812168828795907180705280467750776539375114196966928558377489493879042572629270966563128083318107071076192216334734149460990316097204458249588890919057189841037822035446738534624520372738900054814544125708021194957061940434862050063950301479992691394116572263840672391741275351726658139959802667641147451123698154577014434496619769778914672026310981)
2⅄2Θn21=(1Θn21/1Θn22)=(6765/10946)/(10946/17711)=(0.6180339850173579389731408733784030696144710396491869175954686643522748035812168828795907180705280467750776539375114196966928558377489493879042572629270966563128083318107071076192216334734149460990316097204458249588890919057189841037822035446738534624520372738900054814544125708021194957061940434862050063950301479992691394116572263840672391741275351726658139959802667641147451123698154577014434496619769778914672026310981/0.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793348766303427248602563378691208853255039241149568065044322737281915193947264411947377336118796228332674609000056462085709446106939190333690926542826492010614872113375868104567782733894190051380497995595957314663203658743153972107729659533623172039975156682287843712946756253175992321156343515329456270114)
2⅄2Θn22=(1Θn22/1Θn23)=(10946/17711)/(17711/28657)=(0.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793348766303427248602563378691208853255039241149568065044322737281915193947264411947377336118796228332674609000056462085709446106939190333690926542826492010614872113375868104567782733894190051380497995595957314663203658743153972107729659533623172039975156682287843712946756253175992321156343515329456270114/0.618033988205325051470844819764804410789684893743238999197403775691803049865652371148410510520989636040060020239383047771923090344418466692256691209826569424573402659036186621069895662490839934396482534808249293366367728652685207802631119796210350001744774400669993369857277454025194542345674704260739086436123809191471542729525072408137627804724849077014342045573507345500226820672087099138081446069023275290504937711553896081236696095194891300554838259413057891614614230380011864465924555954915029486687371322887950587988973025787765641902502006490560770492375335869072128973723697525909899849949401542380570192274138953833269358271975433576438566493352409533447325260843772900164008793662979376766584080678368286980493422200509474124995638063998325016575356806364937013644135813239348152283909690477021321143176187318979655930488187877307464144886066231636249432948319782252154796384827441811773737655721115259796908259762012771748612904351467355270963464424049970338835188610112712426283281571692780123530027567435530585895243744983773598073769061660327319677565690756185225250375126496144048574519314652615416826604320061416058903583766618976166381686847890567749589978015842551558083539798304079282548766444498726314687510904840004187458561607984087657465889660466901629619290225773807446697142059531702550860173779530306731339637784834420909376417629200544369613009037931395470565655860697211850507729350594968070628467739121331611822591338939875074152912028474718218934291796070768049691174931081411173535261890637540566004815577345849181700806085773109536936874062183759639878563701713368461457933489199846459852741040583452559584045782880273580626025054960393621104791150504239801793628083888753184213281222737899989531353595980039780856335275848832745925951774435565481383257144851170743622849565551174233171650905537913947726558955926998639075967477405171511323585860348256970373730676623512579823428830652196670970443521652650312314617719928813204452664270509823079875772062672296472066161845273406148584987961056635377045747984785567226157657814844540600900303590745716578846355166277000383850368147398541368601039885542799316048434937362599015947238022123739400495515929790278117039466796943155250026171616010049900547859161810377918135185120563911086296541857137872073140942876086122064417070872736155215130683602610182503402310081306487071221691035349129357574065673308441218550441427923369508322573891195868374219213455700177966988868339323725442300310569843319258819834595386816484628537530097358411557385630038036081934605855462888648497749241023135708552884112084307499040374079631503646578497400286143001709878912656593502460131904944690651498761210175524304707401333007642111874934570959974875248630352095474055204662037198590222284258645357155319817147642809784694838957322818159611962173290993474543741494224796733782321945772411627176606064835816728896953623896430191576229193565272010329064451966360749555082527829151690686394249223575391701852950413511532958788428656174756603971106535924904909795163485361342778378755626897442160728617789719789231252399064800921240883553756499284642495725302718358516243849670237638273371253096974561189238231496667480894720312663572600062811878424119761314861988344907003524444289353386607111700457130892975538262902606692954600970094566772516313640646264438008165544195135568970932058484837910458177757615940258924521059427016086819974177338870084098126112293680427120773284014376941061520745367623966221167603028928359563108490072233660187737725512091286596643054053110932756394598178455525700526921869002337997696897791115608751788393760686743204103709390375824405904316571867257563597026904421258331297763199218341068499842970303939700596712845029137732491188889276616533482220748857172767561154342743483267613497574763583068709215898384338904979586139512161077572669853787905223854555605960149352688697351432459782950064556652824789754684719265798932198066789964057647346198136580940084447080992427679101092228774819415849530655686219771783508392364867222668109013504553861185748682695327494155005757755522210978120529015598283141989740726524060438985239208570331856091007432738946854171755592001954147328750392574240150748508217887427155668772027776808458666294448127857068081097114143141291830966256063091042328226960254039152737551034651219597306068325365530236940363610985099626618278256621418850542624838608367938025613288201835502669504833025089855881634504658547649788882297518930802247269428062951460376173360784450570541229019087831943329727466238615347035628293261681264612485605611194472554698677461004292145025648183689848902536901978574170359772481418152632864570611019995114631678124018564399623128729455281432110828069930557978853334263879680357329797257214642146770422584359842272394179432599364902118156122413371951006734829186586174407649090972537250933454304358446452873643437903479080154935966779495411243326237917437275360295913738353630875527794256202672994381826429842621349059566598038873573646927452280420141675681334403461632410929266845796838468785985972013818613253306347489269637435879540775377743657745053564574100568796454618417838573472450012213420804689953589000942178176361796419722929825173605052866664340300799106675506856963394633073943539100394319014551418501587744704609693966570122483162927033534563980877272568656872666364239103883867815891405241302299612660083051261471891684405206406811599260215654115922811180514359493317514045433925393446627351083504902816065882681369298949645810796663991345918972676832885507903828035035069965453466866734131276825906410301148061555640855637366088564748578008863453955403566318874969466447988275116027497644554559095508950692675437065987367833339149248002233311232857591513417315141152249014202463621453746030638238475765083574693792092682416163590047806818578357818334089402240290330460271486896744250968349792371846320270788986983982971001849460864710192972048714101266706214886415186516383431622291237742959835293296576752625885473008340021635202568307917786230240429912412325086366332833164671807935233974247129846110897860906584778588128554977841365111491084202812576333880029312209931255888613602261227623268311407335031580416652126879994416721917856021216456712147119377464493840946365634923404403810587291063265519768293959591024880482953554105454164776494399274173849321282758139372579125519070384199323027532540042572495376347838224517569878214746833234462783962033709041420944271905642600411766758558118435286317479149945911993579230205534424398925218969187284084167917088320480161915064382175384722755347733538053529678612555396587221272289492968559165299926719475171860278465994346930941829221481662421048958369682800013958195205359946958858219632201556338765397634085912691488990473531772341836200579265101022437798792616114736364588058764001814565376696793104651568552186202324039501692431168649893568761559130404438706075304463132916913843040094915727396447639320235893498970583103604703911784206302125135220016051924486163939002686952577031789789580207279198799595212339044561538193111630666154866175803468611508531946819276267578602086750183201312070349303835014132672645426946295843947377604075792999965104511986600132602854450919496109153086505914785218271277523816170569145409498551837247443905503018459713159088529853089995463586558258017238371078619534494189901245768922078375266078096102173988903234811738842167707715392399762710681508880901699410266252573542240988240220539484244687161949959870188784590152493282618557420525526049481802003001011969152388596154517220923334612834560491328471228670132951809331053494783124541996719824126740412464668318386432634260390131555989810517500087238720033499668492863872701259727117283735213036954321806190459573577136476253620406881390236242453850717102278675367275011341033604354956904072303451163764525246885577694804061834804759744565027741912970652894580730711519000593223296227797745751474334368566144397529399448651289388282095125100324528038524618766793453606448686184876295494992497470077119028509613706947691663467913598771678821928324667620476672366263042188645008200439683148968838329204033918414349024671110025473706249781903199916250828767840318246850682206790661967407614195484523851066057158809365948982796524409393865373207244303311581812471647415989112607739819241372090588686882786055762989845412988100638587430645217573367763548173221202498516941759430505635621314164078584639006176501378371776529294762187249188679903688453083016365983878284537809261262518756324807202428725965732630770841330216003070802945179188330948808319084342394528387479498900792127577904176989915203964127438322224936315734375545242000209372928080399204382873294483023345081480964511288690372334857102976585127543008688976515336566981889241721045468820881460027218480650451896569773528282793034860592525386467529748403531423386956066580591129566946993753707645601423735910946714589803538402484558746554070558676763094531877028300240778867292459085040304288655476846843703109187981993928185085668423072896674459992322992637052029172627979202289144013679031301252748019681055239557525211990089681404194437659210664061136894999476567679799001989042816763792441637296297588721778274069162857242558537181142478277558711658582545276895697386327947796349931953798373870258575566179293017412848518686533831175628991171441532609833548522176082632515615730885996440660222633213525491153993788603133614823603308092263670307429249398052831768852287399239278361307882890742227030045015179537285828942317758313850019192518407369927068430051994277139965802421746868129950797361901106186970024775796489513905851973339847157762501308580800502495027392958090518895906759256028195554314827092856893603657047143804306103220853543636807760756534180130509125170115504065324353561084551767456467878703283665422060927522071396168475416128694559793418710960672785008898349443416966186272115015528492165962940991729769340824231426876504867920577869281501901804096730292773144432424887462051156785427644205604215374952018703981575182328924870014307150085493945632829675123006595247234532574938060508776215235370066650382105593746728547998743762431517604773702760233101859929511114212932267857765990857382140489234741947866140907980598108664549673727187074711239836689116097288620581358830303241790836444847681194821509578811459678263600516453222598318037477754126391457584534319712461178769585092647520675576647939421432808737830198555326796245245489758174268067138918937781344872108036430889485989461562619953240046062044177687824964232124786265135917925812192483511881913668562654848728059461911574833374044736015633178630003140593921205988065743099417245350176222214467669330355585022856544648776913145130334647730048504728338625815682032313221900408277209756778448546602924241895522908887880797012946226052971350804340998708866943504204906305614684021356038664200718847053076037268381198311058380151446417978155424503611683009386886275604564329832152702655546637819729908922776285026346093450116899884844889555780437589419688034337160205185469518791220295215828593362878179851345221062916564888159960917053424992148515196985029835642251456886624559444463830826674111037442858638378057717137174163380674878738179153435460794919216945248979306975608053878633492689395261192727780298007467634434867571622989147503227832641239487734235963289946609903339498202882367309906829047004222354049621383955054611438740970792476532784310988589175419618243361133405450675227693059287434134766374707750287887776110548906026450779914157099487036326203021949261960428516592804550371636947342708587779600097707366437519628712007537425410894371357783438601388840422933314722406392853404054855707157064591548312803154552116411348012701957636877551732560979865303416268276511847018180549254981330913912831070942527131241930418396901280664410091775133475241651254492794081725232927382489444114875946540112363471403147573018808668039222528527061450954391597166486373311930767351781414663084063230624280280559723627734933873050214607251282409184492445126845098928708517988624070907631643228530550999755731583906200928219981156436472764071605541403496527898942666713193984017866489862860732107338521129217992113619708971629968245105907806120668597550336741459329308720382454548626862546672715217922322643682171895173954007746798338974770562166311895871863768014795686917681543776389712810133649719091321492131067452978329901943678682346372614021007083784066720173081620546463342289841923439299298600690930662665317374463481871793977038768887182887252678228705028439822730920891928673622500610671040234497679450047108908818089820986146491258680252643333217015039955333775342848169731653697176955019715950727570925079387235230484698328506124158146351676728199043863628432843633318211955194193390794570262065114980633004152563073594584220260320340579963010782705796140559025717974665875702271696269672331367554175245140803294134068464947482290539833199567295948633841644275395191401751753498272673343336706563841295320515057403077782042781868304428237428900443172697770178315943748473322399413755801374882227727954775447534633771853299368391666957462400111665561642879575670865757057612450710123181072687301531911923788254178734689604634120808179502390340928917890916704470112014516523013574344837212548417489618592316013539449349199148550092473043235509648602435705063335310744320759325819171581114561887147991764664828837631294273650417001081760128415395889311512021495620616254318316641658233590396761698712356492305544893045329238929406427748892068255574554210140628816694001465610496562794430680113061381163415570366751579020832606343999720836095892801060822835607355968873224692047318281746170220190529364553163275988414697979551244024147677705272708238824719963708692466064137906968628956275953519209966151376627002128624768817391911225878493910737341661723139198101685452071047213595282130020588337927905921764315873957497295599678961510276721219946260948459364204208395854416024008095753219108769236137767386676902676483930627769829361063614474648427958264996335973758593013923299717346547091461074083121052447918484140000697909760267997347942910981610077816938269881704295634574449523676588617091810028963255051121889939630805736818229402938200090728268834839655232578427609310116201975084621558432494678438077956520221935303765223156645845692152004745786369822381966011794674948529155180235195589210315106256761000802596224308196950134347628851589489479010363959939979760616952228076909655581533307743308790173430575426597340963813378930104337509160065603517465191750706633632271347314792197368880203789649998255225599330006630142722545974805457654325295739260913563876190808528457270474927591862372195275150922985657954426492654499773179327912900861918553930976724709495062288446103918763303904805108699445161740586942108385385769619988135534075444045084970513312628677112049412011026974212234358097497993509439229507624664130927871026276302474090100150050598457619429807725861046166730641728024566423561433506647590466552674739156227099835991206337020623233415919321631713019506577799490525875004361936001674983424643193635062986355864186760651847716090309522978678856823812681020344069511812122692535855113933768363750567051680217747845203615172558188226262344278884740203091740237987228251387095648532644729036535575950029661164811389887287573716718428307219876469972432564469414104756255016226401926230938339672680322434309243814774749624873503855951425480685347384583173395679938583941096416233381023833618313152109432250410021984157448441916460201695920717451233555501273685312489095159995812541438392015912342534110339533098370380709774226192553302857940468297449139826220469693268660362215165579090623582370799455630386990962068604529434344139302788149492270649405031929371532260878668388177408661060124925847087971525281781065708203929231950308825068918588826464738109362459433995184422654150818299193914226890463063125937816240360121436298286631538542066510800153540147258959416547440415954217119726419373974945039606378895208849495760198206371916111246815786718777262100010468646404019960219143664724151167254074048225564434518616742855148829256377150434448825766828349094462086052273441044073001360924032522594828488676414139651743029626269323376487420176571169347803329029556478347349687685382280071186795547335729490176920124227937327703527933838154726593851415012038943364622954252015214432773842342185155459399099696409254283421153644833722999616149631852601458631398960114457200683951565062637400984052761977876260599504484070209721882960533203056844749973828383989950099452140838189622081864814879436088913703458142862127926859057123913877935582929127263844784869316397389817496597689918693512928778308964650870642425934326691558781449558572076630491677426108804131625780786544299822033011131660676274557699689430156680741180165404613183515371462469902641588442614369961963918065394144537111351502250758976864291447115887915692500959625920368496353421502599713856998290121087343406497539868095055309348501238789824475695292598666992357888125065429040025124751369647904525944795337962801409777715741354642844680182852357190215305161042677181840388037826709006525456258505775203266217678054227588372823393935164183271103046376103569808423770806434727989670935548033639250444917472170848309313605750776424608298147049586488467041211571343825243396028893464075095090204836514638657221621244373102557839271382210280210768747600935199078759116446243500715357504274697281641483756150329762361726628746903025438810761768503332519105279687336427399937188121575880238685138011655092996475555710646613392888299542869107024461737097393307045399029905433227483686359353735561991834455804864431029067941515162089541822242384059741075478940572983913180025822661129915901873887706319572879226715985623058938479254632376033778832396971071640436891509927766339812262274487908713403356945946889067243605401821544474299473078130997662002303102208884391248211606239313256795896290609624175594095683428132742436402973095578741668702236800781658931500157029696060299403287154970862267508811110723383466517779251142827232438845657256516732386502425236416931290784101615661095020413860487838922427330146212094776145444394039850647311302648567540217049935443347175210245315280734201067801933210035942352653801863419059915552919007572320898907771225180584150469344313780228216491607635132777331890986495446138814251317304672505844994242244477789021879470984401716858010259273475939561014760791429668143908992567261053145828244407998045852671249607425759849251491782112572844331227972223191541333705551872142931918902885856858708169033743936908957671773039745960847262448965348780402693931674634469763059636389014900373381721743378581149457375161391632061974386711798164497330495166974910144118365495341452350211117702481069197752730571937048539623826639215549429458770980912168056670272533761384652964371706738318735387514394388805527445301322538995707854974351816310151097463098021425829640227518581847367135429388980004885368321875981435600376871270544718567889171930069442021146665736120319642670202742785357853229577415640157727605820567400635097881843877586628048993265170813413825592350909027462749066545695641553547126356562096520919845064033220504588756673762082562724639704086261646369124472205743797327005618173570157378650940433401961126426353072547719579858324318665596538367589070733154203161531214014027986181386746693652510730362564120459224622256342254946435425899431203545381582161426527549987786579195310046410999057821823638203580277070174826394947133335659699200893324493143036605366926056460899605680985448581498412255295390306033429877516837072966465436019122727431343127333635760896116132184108594758697700387339916948738528108315594793593188400739784345884077188819485640506682485954566074606553372648916495097183934117318630701050354189203336008654081027323167114492096171964964930034546533133265868723174093589698851938444359144362633911435251421991136546044596433681125030533552011724883972502355445440904491049307324562934012632166660850751997766688767142408486582684858847750985797536378546253969361761524234916425306207907317583836409952193181421642181665910597759709669539728513103255749031650207628153679729211013016017028998150539135289807027951285898733293785113584813483616568377708762257040164706703423247374114526991659978364797431692082213769759570087587674913633667166835328192064766025752870153889102139093415221411871445022158634888508915797187423666119970687790068744111386397738772376731688592664968419583347873120005583278082143978783543287852880622535506159053634365076595596189412708936734480231706040408975119517046445894545835223505600725826150678717241860627420874480929615800676972467459957427504623652161775482430121785253166765537216037966290958579055728094357399588233241441881564713682520850054088006420769794465575601074781030812715915832082911679519838084935617824615277244652266461946470321387444603412778727710507031440834700073280524828139721534005653069058170778518337578951041630317199986041804794640053041141780367798443661234602365914087308511009526468227658163799420734898977562201207383885263635411941235998185434623303206895348431447813797675960498307568831350106431238440869595561293924695536867083086156959905084272603552360679764106501029416896395296088215793697874864779983948075513836060997313047422968210210419792720801200404787660955438461806888369333845133824196531388491468053180723732421397913249816798687929650696164985867327354573053704156052622395924207000034895488013399867397145549080503890846913494085214781728722476183829430854590501448162752556094496981540286840911470146910004536413441741982761628921380465505810098754231077921624733921903897826011096765188261157832292284607600237289318491119098300589733747426457759011759779460515755312838050040129811215409847506717381442579474473950518197996998988030847611403845482779076665387165439508671528771329867048190668946505216875458003280175873259587535331681613567365739609868444010189482499912761279966500331507136127298740272882716264786963045678193809540426422863523746379593118609763757546149282897721324632724988658966395645043095927696548836235474753114422305195938165195240255434972258087029347105419269288480999406776703772202254248525665631433855602470600551348710611717904874899675471961475381233206546393551313815123704505007502529922880971490386293052308336532086401228321178071675332379523327633736957811354991799560316851031161670795966081585650975328889974526293750218096800083749171232159681753149317793209338032592385804515476148933942841190634051017203475590606134626792755696688418187528352584010887392260180758627909411313117213944237010154587011899361412569354782426632236451826778797501483058240569494364378685835921415360993823498621628223470705237812750811320096311546916983634016121715462190738737481243675192797571274034267369229158669783996929197054820811669051191680915657605471612520501099207872422095823010084796035872561677775063684265624454757999790627071919600795617126705516976654918519035488711309627665142897023414872456991311023484663433018110758278954531179118539972781519349548103430226471717206965139407474613532470251596468576613043933419408870433053006246292354398576264089053285410196461597515441253445929441323236905468122971699759221132707540914959695711344523153156296890812018006071814914331576927103325540007677007362947970827372020797710855986320968698747251980318944760442474788009910318595805562340789335938863105000523432320200998010957183236207558362703702411278221725930837142757441462818857521722441288341417454723104302613672052203650068046201626129741424433820706982587151481313466168824371008828558467390166451477823917367484384269114003559339777366786474508846006211396866385176396691907736329692570750601947168231147712600760721638692117109257772969954984820462714171057682241686149980807481592630072931569948005722860034197578253131870049202638098893813029975224203510486094148026660152842237498691419199497504972607041909481104093240743971804445685172907143106396342952856195693896779146456363192239243465819869490874829884495934675646438915448232543532121296716334577939072477928603831524583871305440206581289039327214991101650556583033813727884984471507834037059008270230659175768573123495132079422130718498098195903269707226855567575112537948843214572355794395784625047981296018424817671075129985692849914506054367170324876993404752765467425061939491223784764629933349617894406253271452001256237568482395226297239766898140070488885787067732142234009142617859510765258052133859092019401891335450326272812925288760163310883902711379418641169696758209163555152318805178490421188540321736399483546777401681962522245873608542415465680287538821230414907352479324423352060578567191262169801444673203754754510241825731932861081062218655127891963569110514010538437380046759953937955822312175035767875213734864082074187807516488118086331437345151271940538088425166625955263984366821369996859406078794011934256900582754649823777785532330669644414977143455351223086854869665352269951495271661374184317967686778099591722790243221551453397075758104477091112119202987053773947028649195659001291133056495795093694385315978643961335799281152946923962731618801688941619848553582021844575496388316990613113724395435670167847297344453362180270091077223714973653906549883100115155110444219562410580311965662839794814530481208779704784171406637121820148654778937083435111840039082946575007851484803014970164357748543113375440555536169173325888962557141361621942282862825836619325121261820846564539205080783054751020693024391946121366507310604738807272219701992532365565132428377010852496772167358760512265764036710053390096660501797117632690093170952995777645950378616044945388561259029207523467215689011410824580381756638866594549324772306940712565865233625292249712112223889451093973549220085842900512963673796978050738039571483407195449628363052657291412220399902292633562480371287992462574589105628642216561398611159577066685277593607146595945144292842935408451687196845447883588651987298042363122448267439020134696583731723488152981819450745018669086087168929057472868758069581603098719335589908224866524758348745507205918274767072617510555885124053459887636528596852426981191331960777471472938549045608402833513626688069232648218585336915936769375719719440276372265066126949785392748717590815507554873154901071291482011375929092368356771469449000244268416093799071780018843563527235928394458596503472101057333286806015982133510137139267892661478870782007886380291028370031754894092193879331402449663258540670691279617545451373137453327284782077677356317828104826045992253201661025229437833688104128136231985204313082318456223610287189866350280908678507868932547021670098056321317653627385978992916215933279826918379453536657710158076560700701399309069337334682625536518128206022961231112817112747321771294971560177269079108071326377499389328959765502320549952891091181910179013853508741319747356666782984960044666224657151830268346302823044980284049272429074920612764769515301671493875841853648323271800956136371567156366681788044805806609205429737934885019366995847436926405415779739679659420036989217294203859440974282025334124297728303730327668632445824754859196705865931535052517709460166800432704051366158355724604808598248246501727326656663293436158704679484942596922217957218131695571762571099556827302229821684056251526677600586244198625117772272045224552465366228146700631608333042537599888334438357120424329134242942387549289876818927312698468088076211745821265310395365879191820497609659071082109083295529887985483476986425655162787451582510381407683986460550650800851449907526956764490351397564294936664689255679240674180828418885438112852008235335171162368705726349582998918239871584604110688487978504379383745681683358341766409603238301287643507694455106954670761070593572251107931744425445789859371183305998534389503437205569319886938618836584429633248420979167393656000279163904107198939177164392644031126775307952681718253829779809470635446836724011585302020448755975852322294727291761175280036291307533935862093031371043724046480790033848623372997871375231182608088774121506089262658338276860801898314547928952786404717869979411662072094078235684126042502704400321038489723278780053739051540635795791604145583975991904246780891230763862232613323097323516069372230170638936385525351572041735003664026241406986076700282653452908538925916878947552081515859999302090239732002652057089018389922183061730118295704365425550476323411382908189971036744948878110060369194263181770597061799909271731165160344767421572390689883798024915378441567505321561922043479778064696234776843354154307847995254213630177)
2⅄2Θn23=(1Θn23/1Θn24)=(17711/28657)/(28657/46368)=(0.618033988205325051470844819764804410789684893743238999197403775691803049865652371148410510520989636040060020239383047771923090344418466692256691209826569424573402659036186621069895662490839934396482534808249293366367728652685207802631119796210350001744774400669993369857277454025194542345674704260739086436123809191471542729525072408137627804724849077014342045573507345500226820672087099138081446069023275290504937711553896081236696095194891300554838259413057891614614230380011864465924555954915029486687371322887950587988973025787765641902502006490560770492375335869072128973723697525909899849949401542380570192274138953833269358271975433576438566493352409533447325260843772900164008793662979376766584080678368286980493422200509474124995638063998325016575356806364937013644135813239348152283909690477021321143176187318979655930488187877307464144886066231636249432948319782252154796384827441811773737655721115259796908259762012771748612904351467355270963464424049970338835188610112712426283281571692780123530027567435530585895243744983773598073769061660327319677565690756185225250375126496144048574519314652615416826604320061416058903583766618976166381686847890567749589978015842551558083539798304079282548766444498726314687510904840004187458561607984087657465889660466901629619290225773807446697142059531702550860173779530306731339637784834420909376417629200544369613009037931395470565655860697211850507729350594968070628467739121331611822591338939875074152912028474718218934291796070768049691174931081411173535261890637540566004815577345849181700806085773109536936874062183759639878563701713368461457933489199846459852741040583452559584045782880273580626025054960393621104791150504239801793628083888753184213281222737899989531353595980039780856335275848832745925951774435565481383257144851170743622849565551174233171650905537913947726558955926998639075967477405171511323585860348256970373730676623512579823428830652196670970443521652650312314617719928813204452664270509823079875772062672296472066161845273406148584987961056635377045747984785567226157657814844540600900303590745716578846355166277000383850368147398541368601039885542799316048434937362599015947238022123739400495515929790278117039466796943155250026171616010049900547859161810377918135185120563911086296541857137872073140942876086122064417070872736155215130683602610182503402310081306487071221691035349129357574065673308441218550441427923369508322573891195868374219213455700177966988868339323725442300310569843319258819834595386816484628537530097358411557385630038036081934605855462888648497749241023135708552884112084307499040374079631503646578497400286143001709878912656593502460131904944690651498761210175524304707401333007642111874934570959974875248630352095474055204662037198590222284258645357155319817147642809784694838957322818159611962173290993474543741494224796733782321945772411627176606064835816728896953623896430191576229193565272010329064451966360749555082527829151690686394249223575391701852950413511532958788428656174756603971106535924904909795163485361342778378755626897442160728617789719789231252399064800921240883553756499284642495725302718358516243849670237638273371253096974561189238231496667480894720312663572600062811878424119761314861988344907003524444289353386607111700457130892975538262902606692954600970094566772516313640646264438008165544195135568970932058484837910458177757615940258924521059427016086819974177338870084098126112293680427120773284014376941061520745367623966221167603028928359563108490072233660187737725512091286596643054053110932756394598178455525700526921869002337997696897791115608751788393760686743204103709390375824405904316571867257563597026904421258331297763199218341068499842970303939700596712845029137732491188889276616533482220748857172767561154342743483267613497574763583068709215898384338904979586139512161077572669853787905223854555605960149352688697351432459782950064556652824789754684719265798932198066789964057647346198136580940084447080992427679101092228774819415849530655686219771783508392364867222668109013504553861185748682695327494155005757755522210978120529015598283141989740726524060438985239208570331856091007432738946854171755592001954147328750392574240150748508217887427155668772027776808458666294448127857068081097114143141291830966256063091042328226960254039152737551034651219597306068325365530236940363610985099626618278256621418850542624838608367938025613288201835502669504833025089855881634504658547649788882297518930802247269428062951460376173360784450570541229019087831943329727466238615347035628293261681264612485605611194472554698677461004292145025648183689848902536901978574170359772481418152632864570611019995114631678124018564399623128729455281432110828069930557978853334263879680357329797257214642146770422584359842272394179432599364902118156122413371951006734829186586174407649090972537250933454304358446452873643437903479080154935966779495411243326237917437275360295913738353630875527794256202672994381826429842621349059566598038873573646927452280420141675681334403461632410929266845796838468785985972013818613253306347489269637435879540775377743657745053564574100568796454618417838573472450012213420804689953589000942178176361796419722929825173605052866664340300799106675506856963394633073943539100394319014551418501587744704609693966570122483162927033534563980877272568656872666364239103883867815891405241302299612660083051261471891684405206406811599260215654115922811180514359493317514045433925393446627351083504902816065882681369298949645810796663991345918972676832885507903828035035069965453466866734131276825906410301148061555640855637366088564748578008863453955403566318874969466447988275116027497644554559095508950692675437065987367833339149248002233311232857591513417315141152249014202463621453746030638238475765083574693792092682416163590047806818578357818334089402240290330460271486896744250968349792371846320270788986983982971001849460864710192972048714101266706214886415186516383431622291237742959835293296576752625885473008340021635202568307917786230240429912412325086366332833164671807935233974247129846110897860906584778588128554977841365111491084202812576333880029312209931255888613602261227623268311407335031580416652126879994416721917856021216456712147119377464493840946365634923404403810587291063265519768293959591024880482953554105454164776494399274173849321282758139372579125519070384199323027532540042572495376347838224517569878214746833234462783962033709041420944271905642600411766758558118435286317479149945911993579230205534424398925218969187284084167917088320480161915064382175384722755347733538053529678612555396587221272289492968559165299926719475171860278465994346930941829221481662421048958369682800013958195205359946958858219632201556338765397634085912691488990473531772341836200579265101022437798792616114736364588058764001814565376696793104651568552186202324039501692431168649893568761559130404438706075304463132916913843040094915727396447639320235893498970583103604703911784206302125135220016051924486163939002686952577031789789580207279198799595212339044561538193111630666154866175803468611508531946819276267578602086750183201312070349303835014132672645426946295843947377604075792999965104511986600132602854450919496109153086505914785218271277523816170569145409498551837247443905503018459713159088529853089995463586558258017238371078619534494189901245768922078375266078096102173988903234811738842167707715392399762710681508880901699410266252573542240988240220539484244687161949959870188784590152493282618557420525526049481802003001011969152388596154517220923334612834560491328471228670132951809331053494783124541996719824126740412464668318386432634260390131555989810517500087238720033499668492863872701259727117283735213036954321806190459573577136476253620406881390236242453850717102278675367275011341033604354956904072303451163764525246885577694804061834804759744565027741912970652894580730711519000593223296227797745751474334368566144397529399448651289388282095125100324528038524618766793453606448686184876295494992497470077119028509613706947691663467913598771678821928324667620476672366263042188645008200439683148968838329204033918414349024671110025473706249781903199916250828767840318246850682206790661967407614195484523851066057158809365948982796524409393865373207244303311581812471647415989112607739819241372090588686882786055762989845412988100638587430645217573367763548173221202498516941759430505635621314164078584639006176501378371776529294762187249188679903688453083016365983878284537809261262518756324807202428725965732630770841330216003070802945179188330948808319084342394528387479498900792127577904176989915203964127438322224936315734375545242000209372928080399204382873294483023345081480964511288690372334857102976585127543008688976515336566981889241721045468820881460027218480650451896569773528282793034860592525386467529748403531423386956066580591129566946993753707645601423735910946714589803538402484558746554070558676763094531877028300240778867292459085040304288655476846843703109187981993928185085668423072896674459992322992637052029172627979202289144013679031301252748019681055239557525211990089681404194437659210664061136894999476567679799001989042816763792441637296297588721778274069162857242558537181142478277558711658582545276895697386327947796349931953798373870258575566179293017412848518686533831175628991171441532609833548522176082632515615730885996440660222633213525491153993788603133614823603308092263670307429249398052831768852287399239278361307882890742227030045015179537285828942317758313850019192518407369927068430051994277139965802421746868129950797361901106186970024775796489513905851973339847157762501308580800502495027392958090518895906759256028195554314827092856893603657047143804306103220853543636807760756534180130509125170115504065324353561084551767456467878703283665422060927522071396168475416128694559793418710960672785008898349443416966186272115015528492165962940991729769340824231426876504867920577869281501901804096730292773144432424887462051156785427644205604215374952018703981575182328924870014307150085493945632829675123006595247234532574938060508776215235370066650382105593746728547998743762431517604773702760233101859929511114212932267857765990857382140489234741947866140907980598108664549673727187074711239836689116097288620581358830303241790836444847681194821509578811459678263600516453222598318037477754126391457584534319712461178769585092647520675576647939421432808737830198555326796245245489758174268067138918937781344872108036430889485989461562619953240046062044177687824964232124786265135917925812192483511881913668562654848728059461911574833374044736015633178630003140593921205988065743099417245350176222214467669330355585022856544648776913145130334647730048504728338625815682032313221900408277209756778448546602924241895522908887880797012946226052971350804340998708866943504204906305614684021356038664200718847053076037268381198311058380151446417978155424503611683009386886275604564329832152702655546637819729908922776285026346093450116899884844889555780437589419688034337160205185469518791220295215828593362878179851345221062916564888159960917053424992148515196985029835642251456886624559444463830826674111037442858638378057717137174163380674878738179153435460794919216945248979306975608053878633492689395261192727780298007467634434867571622989147503227832641239487734235963289946609903339498202882367309906829047004222354049621383955054611438740970792476532784310988589175419618243361133405450675227693059287434134766374707750287887776110548906026450779914157099487036326203021949261960428516592804550371636947342708587779600097707366437519628712007537425410894371357783438601388840422933314722406392853404054855707157064591548312803154552116411348012701957636877551732560979865303416268276511847018180549254981330913912831070942527131241930418396901280664410091775133475241651254492794081725232927382489444114875946540112363471403147573018808668039222528527061450954391597166486373311930767351781414663084063230624280280559723627734933873050214607251282409184492445126845098928708517988624070907631643228530550999755731583906200928219981156436472764071605541403496527898942666713193984017866489862860732107338521129217992113619708971629968245105907806120668597550336741459329308720382454548626862546672715217922322643682171895173954007746798338974770562166311895871863768014795686917681543776389712810133649719091321492131067452978329901943678682346372614021007083784066720173081620546463342289841923439299298600690930662665317374463481871793977038768887182887252678228705028439822730920891928673622500610671040234497679450047108908818089820986146491258680252643333217015039955333775342848169731653697176955019715950727570925079387235230484698328506124158146351676728199043863628432843633318211955194193390794570262065114980633004152563073594584220260320340579963010782705796140559025717974665875702271696269672331367554175245140803294134068464947482290539833199567295948633841644275395191401751753498272673343336706563841295320515057403077782042781868304428237428900443172697770178315943748473322399413755801374882227727954775447534633771853299368391666957462400111665561642879575670865757057612450710123181072687301531911923788254178734689604634120808179502390340928917890916704470112014516523013574344837212548417489618592316013539449349199148550092473043235509648602435705063335310744320759325819171581114561887147991764664828837631294273650417001081760128415395889311512021495620616254318316641658233590396761698712356492305544893045329238929406427748892068255574554210140628816694001465610496562794430680113061381163415570366751579020832606343999720836095892801060822835607355968873224692047318281746170220190529364553163275988414697979551244024147677705272708238824719963708692466064137906968628956275953519209966151376627002128624768817391911225878493910737341661723139198101685452071047213595282130020588337927905921764315873957497295599678961510276721219946260948459364204208395854416024008095753219108769236137767386676902676483930627769829361063614474648427958264996335973758593013923299717346547091461074083121052447918484140000697909760267997347942910981610077816938269881704295634574449523676588617091810028963255051121889939630805736818229402938200090728268834839655232578427609310116201975084621558432494678438077956520221935303765223156645845692152004745786369822381966011794674948529155180235195589210315106256761000802596224308196950134347628851589489479010363959939979760616952228076909655581533307743308790173430575426597340963813378930104337509160065603517465191750706633632271347314792197368880203789649998255225599330006630142722545974805457654325295739260913563876190808528457270474927591862372195275150922985657954426492654499773179327912900861918553930976724709495062288446103918763303904805108699445161740586942108385385769619988135534075444045084970513312628677112049412011026974212234358097497993509439229507624664130927871026276302474090100150050598457619429807725861046166730641728024566423561433506647590466552674739156227099835991206337020623233415919321631713019506577799490525875004361936001674983424643193635062986355864186760651847716090309522978678856823812681020344069511812122692535855113933768363750567051680217747845203615172558188226262344278884740203091740237987228251387095648532644729036535575950029661164811389887287573716718428307219876469972432564469414104756255016226401926230938339672680322434309243814774749624873503855951425480685347384583173395679938583941096416233381023833618313152109432250410021984157448441916460201695920717451233555501273685312489095159995812541438392015912342534110339533098370380709774226192553302857940468297449139826220469693268660362215165579090623582370799455630386990962068604529434344139302788149492270649405031929371532260878668388177408661060124925847087971525281781065708203929231950308825068918588826464738109362459433995184422654150818299193914226890463063125937816240360121436298286631538542066510800153540147258959416547440415954217119726419373974945039606378895208849495760198206371916111246815786718777262100010468646404019960219143664724151167254074048225564434518616742855148829256377150434448825766828349094462086052273441044073001360924032522594828488676414139651743029626269323376487420176571169347803329029556478347349687685382280071186795547335729490176920124227937327703527933838154726593851415012038943364622954252015214432773842342185155459399099696409254283421153644833722999616149631852601458631398960114457200683951565062637400984052761977876260599504484070209721882960533203056844749973828383989950099452140838189622081864814879436088913703458142862127926859057123913877935582929127263844784869316397389817496597689918693512928778308964650870642425934326691558781449558572076630491677426108804131625780786544299822033011131660676274557699689430156680741180165404613183515371462469902641588442614369961963918065394144537111351502250758976864291447115887915692500959625920368496353421502599713856998290121087343406497539868095055309348501238789824475695292598666992357888125065429040025124751369647904525944795337962801409777715741354642844680182852357190215305161042677181840388037826709006525456258505775203266217678054227588372823393935164183271103046376103569808423770806434727989670935548033639250444917472170848309313605750776424608298147049586488467041211571343825243396028893464075095090204836514638657221621244373102557839271382210280210768747600935199078759116446243500715357504274697281641483756150329762361726628746903025438810761768503332519105279687336427399937188121575880238685138011655092996475555710646613392888299542869107024461737097393307045399029905433227483686359353735561991834455804864431029067941515162089541822242384059741075478940572983913180025822661129915901873887706319572879226715985623058938479254632376033778832396971071640436891509927766339812262274487908713403356945946889067243605401821544474299473078130997662002303102208884391248211606239313256795896290609624175594095683428132742436402973095578741668702236800781658931500157029696060299403287154970862267508811110723383466517779251142827232438845657256516732386502425236416931290784101615661095020413860487838922427330146212094776145444394039850647311302648567540217049935443347175210245315280734201067801933210035942352653801863419059915552919007572320898907771225180584150469344313780228216491607635132777331890986495446138814251317304672505844994242244477789021879470984401716858010259273475939561014760791429668143908992567261053145828244407998045852671249607425759849251491782112572844331227972223191541333705551872142931918902885856858708169033743936908957671773039745960847262448965348780402693931674634469763059636389014900373381721743378581149457375161391632061974386711798164497330495166974910144118365495341452350211117702481069197752730571937048539623826639215549429458770980912168056670272533761384652964371706738318735387514394388805527445301322538995707854974351816310151097463098021425829640227518581847367135429388980004885368321875981435600376871270544718567889171930069442021146665736120319642670202742785357853229577415640157727605820567400635097881843877586628048993265170813413825592350909027462749066545695641553547126356562096520919845064033220504588756673762082562724639704086261646369124472205743797327005618173570157378650940433401961126426353072547719579858324318665596538367589070733154203161531214014027986181386746693652510730362564120459224622256342254946435425899431203545381582161426527549987786579195310046410999057821823638203580277070174826394947133335659699200893324493143036605366926056460899605680985448581498412255295390306033429877516837072966465436019122727431343127333635760896116132184108594758697700387339916948738528108315594793593188400739784345884077188819485640506682485954566074606553372648916495097183934117318630701050354189203336008654081027323167114492096171964964930034546533133265868723174093589698851938444359144362633911435251421991136546044596433681125030533552011724883972502355445440904491049307324562934012632166660850751997766688767142408486582684858847750985797536378546253969361761524234916425306207907317583836409952193181421642181665910597759709669539728513103255749031650207628153679729211013016017028998150539135289807027951285898733293785113584813483616568377708762257040164706703423247374114526991659978364797431692082213769759570087587674913633667166835328192064766025752870153889102139093415221411871445022158634888508915797187423666119970687790068744111386397738772376731688592664968419583347873120005583278082143978783543287852880622535506159053634365076595596189412708936734480231706040408975119517046445894545835223505600725826150678717241860627420874480929615800676972467459957427504623652161775482430121785253166765537216037966290958579055728094357399588233241441881564713682520850054088006420769794465575601074781030812715915832082911679519838084935617824615277244652266461946470321387444603412778727710507031440834700073280524828139721534005653069058170778518337578951041630317199986041804794640053041141780367798443661234602365914087308511009526468227658163799420734898977562201207383885263635411941235998185434623303206895348431447813797675960498307568831350106431238440869595561293924695536867083086156959905084272603552360679764106501029416896395296088215793697874864779983948075513836060997313047422968210210419792720801200404787660955438461806888369333845133824196531388491468053180723732421397913249816798687929650696164985867327354573053704156052622395924207000034895488013399867397145549080503890846913494085214781728722476183829430854590501448162752556094496981540286840911470146910004536413441741982761628921380465505810098754231077921624733921903897826011096765188261157832292284607600237289318491119098300589733747426457759011759779460515755312838050040129811215409847506717381442579474473950518197996998988030847611403845482779076665387165439508671528771329867048190668946505216875458003280175873259587535331681613567365739609868444010189482499912761279966500331507136127298740272882716264786963045678193809540426422863523746379593118609763757546149282897721324632724988658966395645043095927696548836235474753114422305195938165195240255434972258087029347105419269288480999406776703772202254248525665631433855602470600551348710611717904874899675471961475381233206546393551313815123704505007502529922880971490386293052308336532086401228321178071675332379523327633736957811354991799560316851031161670795966081585650975328889974526293750218096800083749171232159681753149317793209338032592385804515476148933942841190634051017203475590606134626792755696688418187528352584010887392260180758627909411313117213944237010154587011899361412569354782426632236451826778797501483058240569494364378685835921415360993823498621628223470705237812750811320096311546916983634016121715462190738737481243675192797571274034267369229158669783996929197054820811669051191680915657605471612520501099207872422095823010084796035872561677775063684265624454757999790627071919600795617126705516976654918519035488711309627665142897023414872456991311023484663433018110758278954531179118539972781519349548103430226471717206965139407474613532470251596468576613043933419408870433053006246292354398576264089053285410196461597515441253445929441323236905468122971699759221132707540914959695711344523153156296890812018006071814914331576927103325540007677007362947970827372020797710855986320968698747251980318944760442474788009910318595805562340789335938863105000523432320200998010957183236207558362703702411278221725930837142757441462818857521722441288341417454723104302613672052203650068046201626129741424433820706982587151481313466168824371008828558467390166451477823917367484384269114003559339777366786474508846006211396866385176396691907736329692570750601947168231147712600760721638692117109257772969954984820462714171057682241686149980807481592630072931569948005722860034197578253131870049202638098893813029975224203510486094148026660152842237498691419199497504972607041909481104093240743971804445685172907143106396342952856195693896779146456363192239243465819869490874829884495934675646438915448232543532121296716334577939072477928603831524583871305440206581289039327214991101650556583033813727884984471507834037059008270230659175768573123495132079422130718498098195903269707226855567575112537948843214572355794395784625047981296018424817671075129985692849914506054367170324876993404752765467425061939491223784764629933349617894406253271452001256237568482395226297239766898140070488885787067732142234009142617859510765258052133859092019401891335450326272812925288760163310883902711379418641169696758209163555152318805178490421188540321736399483546777401681962522245873608542415465680287538821230414907352479324423352060578567191262169801444673203754754510241825731932861081062218655127891963569110514010538437380046759953937955822312175035767875213734864082074187807516488118086331437345151271940538088425166625955263984366821369996859406078794011934256900582754649823777785532330669644414977143455351223086854869665352269951495271661374184317967686778099591722790243221551453397075758104477091112119202987053773947028649195659001291133056495795093694385315978643961335799281152946923962731618801688941619848553582021844575496388316990613113724395435670167847297344453362180270091077223714973653906549883100115155110444219562410580311965662839794814530481208779704784171406637121820148654778937083435111840039082946575007851484803014970164357748543113375440555536169173325888962557141361621942282862825836619325121261820846564539205080783054751020693024391946121366507310604738807272219701992532365565132428377010852496772167358760512265764036710053390096660501797117632690093170952995777645950378616044945388561259029207523467215689011410824580381756638866594549324772306940712565865233625292249712112223889451093973549220085842900512963673796978050738039571483407195449628363052657291412220399902292633562480371287992462574589105628642216561398611159577066685277593607146595945144292842935408451687196845447883588651987298042363122448267439020134696583731723488152981819450745018669086087168929057472868758069581603098719335589908224866524758348745507205918274767072617510555885124053459887636528596852426981191331960777471472938549045608402833513626688069232648218585336915936769375719719440276372265066126949785392748717590815507554873154901071291482011375929092368356771469449000244268416093799071780018843563527235928394458596503472101057333286806015982133510137139267892661478870782007886380291028370031754894092193879331402449663258540670691279617545451373137453327284782077677356317828104826045992253201661025229437833688104128136231985204313082318456223610287189866350280908678507868932547021670098056321317653627385978992916215933279826918379453536657710158076560700701399309069337334682625536518128206022961231112817112747321771294971560177269079108071326377499389328959765502320549952891091181910179013853508741319747356666782984960044666224657151830268346302823044980284049272429074920612764769515301671493875841853648323271800956136371567156366681788044805806609205429737934885019366995847436926405415779739679659420036989217294203859440974282025334124297728303730327668632445824754859196705865931535052517709460166800432704051366158355724604808598248246501727326656663293436158704679484942596922217957218131695571762571099556827302229821684056251526677600586244198625117772272045224552465366228146700631608333042537599888334438357120424329134242942387549289876818927312698468088076211745821265310395365879191820497609659071082109083295529887985483476986425655162787451582510381407683986460550650800851449907526956764490351397564294936664689255679240674180828418885438112852008235335171162368705726349582998918239871584604110688487978504379383745681683358341766409603238301287643507694455106954670761070593572251107931744425445789859371183305998534389503437205569319886938618836584429633248420979167393656000279163904107198939177164392644031126775307952681718253829779809470635446836724011585302020448755975852322294727291761175280036291307533935862093031371043724046480790033848623372997871375231182608088774121506089262658338276860801898314547928952786404717869979411662072094078235684126042502704400321038489723278780053739051540635795791604145583975991904246780891230763862232613323097323516069372230170638936385525351572041735003664026241406986076700282653452908538925916878947552081515859999302090239732002652057089018389922183061730118295704365425550476323411382908189971036744948878110060369194263181770597061799909271731165160344767421572390689883798024915378441567505321561922043479778064696234776843354154307847995254213630177/0.61803398895790200138026224982746721877156659765355417529330572808833678)
2⅄2Θn24=(1Θn24/1Θn25)=(28657/46368)/(46368/75025)=(0.61803398895790200138026224982746721877156659765355417529330572808833678/0.61803398867044318560479840053315561479506831056314561812729090303232255914695101632789070309896701099633455514828390536487837387537487504165278240586471176274575141619460179940019993335554815061646117960679773408863712095968010663112295901366211262912362545818060646451182939020326557814061979340219926691102965678107297567477507497500833055648117294235254915028323892035988003998667110963012329223592135954681772742419193602132622459180273242252582472509163612129290236587804065311562812395868043985338220593135621459513495501499500166611129623458847050983005664778407197600799733422192602465844718427190936354548483838720426524491836054648450516494501832722425858047317560813062312562479173608797067644118627124291902699100299900033322225924691769410196601132955681439520159946684438520493168943685438187270909696767744085304898367210929690103298900366544485171609463512162612462512495834721759413528823725424858380539820059980006664445184938353882039320226591136287904031989336887704098633788737087637454181939353548817060979673442185938020659780073308897034321892702432522492502499166944351882705764745084971676107964011996001332889036987670776407864045318227257580806397867377540819726757747417527490836387870709763412195934688437187604131956014661779406864378540486504498500499833388870376541152949016994335221592802399200266577807397534155281572809063645451516161279573475508163945351549483505498167277574141952682439186937687437520826391202932355881372875708097300899700099966677774075308230589)
2⅄2Θn25=(1Θn25/1Θn26)=(46368/75025)/(75025/121393)=(0.61803398867044318560479840053315561479506831056314561812729090303232255914695101632789070309896701099633455514828390536487837387537487504165278240586471176274575141619460179940019993335554815061646117960679773408863712095968010663112295901366211262912362545818060646451182939020326557814061979340219926691102965678107297567477507497500833055648117294235254915028323892035988003998667110963012329223592135954681772742419193602132622459180273242252582472509163612129290236587804065311562812395868043985338220593135621459513495501499500166611129623458847050983005664778407197600799733422192602465844718427190936354548483838720426524491836054648450516494501832722425858047317560813062312562479173608797067644118627124291902699100299900033322225924691769410196601132955681439520159946684438520493168943685438187270909696767744085304898367210929690103298900366544485171609463512162612462512495834721759413528823725424858380539820059980006664445184938353882039320226591136287904031989336887704098633788737087637454181939353548817060979673442185938020659780073308897034321892702432522492502499166944351882705764745084971676107964011996001332889036987670776407864045318227257580806397867377540819726757747417527490836387870709763412195934688437187604131956014661779406864378540486504498500499833388870376541152949016994335221592802399200266577807397534155281572809063645451516161279573475508163945351549483505498167277574141952682439186937687437520826391202932355881372875708097300899700099966677774075308230589/0.6180339887802426828565073768668704126267577207911494072969611097839249380112527081462687304869308773982025322712182745298328569192622309358859242295684265155321970789089980476633743296565699834422083645679734416317250582817790152644715922664404043066733666685887983656388753882019556317085828672163963325727183610257593106686547000238893511157974512533671628512352442068323544191180710584630085754532798431540533638677683227204204525796380351420592620661817402980402494377764780506289489509279777252395113392040727224798793999654016294185002430123647986292455083901048660136910695015363324079642153995699916799156458774393910686777656042770176204558747209476658456418409628232270394503801701910324318535665153674429332828087286746352755101200233950886789188832964009456887958943266909953621708006227706704669956257774336246735808489781124117535607489723460166566441228077401497615183742060909607638002191230136828317942550229420147784468626691819132898931569365614162266358027233860272009094428838565650408178395788884037794601006647829776016739021195620834809255887901279315940787360061947558755447183939765884359065184977717001804057894606773042926692642903627062515960557857537090277034095870437339879564719547255607819231751418945079205555509790515103836300280905818292652788875800087319697181880339064031698697618478824973433394017776972313065827518884943942401950689084214081536826670401093967526957897078085227319532427734712874712709958564332375013386274332127882167835048149399059253828474458988574300000823770728130946594943695270732249800235598428245450726153896847429423442867381150478198907680014498364815104660071009036764887596484146532337119932780308584514757852594465908248416300775168255171220745842017249759047062021698120978969133310816933431087459738205662599985172126893642961291013485126819503595759228291581886929229856746270378028387139291392419661759739029433328116118721837338232023263285362417931841209954445478734358653299613651528506586046971406918026574843689504337152883609433822378555600405295198240425724712298073200266901715914426696761757267717248935276333890751526035273862578567133195489031492754936446088324697470200093909863006927911823581260863476477226858220819981382781544240606954272486881451154514675475521652813588921931248095030191197185999192704686431672336955178634682395195769113540319458288369181089519165025989966472531365070473585791602481197433130411143970410155445536398309622465875297587175537304457423409916552025240335109932203669074823095236133879218735841440610249355399405237534289456558450652014531315644229897934806784575716886476155956274249750809354740388655029532180603494435428731475455751155338446203652599408532617201980344830426795614244643430840328519766378621502063545673968021220333956653184285749590174062754854069015511602810705724382789781947888263738436318403861837173477877637096043429192787063504485431614673004209468420749137100162282833441796479203907968334253210646412890364353793052317678943596418244874086644205184812962856177868575)
Continued base chain ratios abbreviated
2⅄2Θn26=(1Θn26/1Θn27)=(75025/121393)/(121393/196418)
2⅄2Θn27=(1Θn27/1Θn28)=(121393/196418)/(196418/317811)
2⅄2Θn28=(1Θn28/1Θn29)=(196418/317811)/(317811/514229)
2⅄2Θn29=(1Θn29/1Θn30)=(317811/514229)/(514229/832040)
2⅄2Θn30=(1Θn30/1Θn31)=(514229/832040)/(832040/1346296)
2⅄2Θn31=(1Θn31/1Θn32)=(832040/1346296)/(1346296/2178309)
2⅄2Θn32=(1Θn32/1Θn33)=(1346296/2178309)/(2178309/3524578)
2⅄2Θn33=(1Θn33/1Θn34)=(2178309/3524578)/(3524578/5702887)
2⅄2Θn34=(1Θn34/1Θn35)=(3524578/5702887)/(5702887/9227465)
2⅄2Θn35=(1Θn35/1Θn36)=(5702887/9227465)/(9227465/14930352)
2⅄2Θn36=(1Θn36/1Θn37)=(9227465/14930352)/(14930352/24157817)
2⅄2Θn37=(1Θn37/1Θn38)=(14930352/24157817)/(24157817/39088169)
2⅄2Θn38=(1Θn38/1Θn39)=(24157817/39088169)/(39088169/63245986)
2⅄2Θn39=(1Θn39/1Θn40)=(39088169/63245986)/(63245986/102334155)
2⅄2Θn40=(1Θn40/1Θn41)=(63245986/102334155)/(102334155/165780141)
2⅄2Θn41=(1Θn41/1Θn42)=(102334155/165780141)/(165780141/269114296)
2⅄2Θn42=(1Θn42/1Θn43)=(165780141/269114296)/(269114296/434894437)
2⅄2Θn43=(1Θn43/1Θn44)=(269114296/434894437)/(434894437/704008733)
2⅄2Θn44=(1Θn44/1Θn45)=(434894437/704008733)/(704008733/1138903170)
And so on for 2⅄2Θn45 2⅄2Θn46 . . . of ∈2⅄2Θ
then if ∈1⅄3Θn1 of (2⅄2Θn2/2⅄2Θn1)=(2/0)=0
1⅄3Θn1 of (2⅄2Θn2/2⅄2Θn1)=(2/0)=0
1⅄3Θn2 of (2⅄2Θn3/2⅄2Θn2)=(0.83/2)=0.415
1⅄3Θn3 of (2⅄2Θn4/2⅄2Θn3)=(1/0.8^3)=1.2048192771084337349397590361445783132530 or 1.204819277108433734939759036144578313253012048192771084337349397590361445783132530
1⅄3Θn4 of (2⅄2Θn5/2⅄2Θn4)=(0.96/1)=0.96
1⅄3Θn5 of (2⅄2Θn6/2⅄2Θn5)=(1.015626/0.96)=1.05794375
1⅄3Θn6 of (2⅄2Θn7/2⅄2Θn6)=(0.994082840236686390532544378698224852071005917159763313609467455621301775147928/1.015626)
1⅄3Θn7 of (2⅄2Θn8/2⅄2Θn7)
And so on for ∈1⅄3Θn1 of (2⅄2Θn2/2⅄2Θn1)
then if 1⅄4Θn1 from 1⅄3Θn2 of (2⅄2Θn3/2⅄2Θn2)/1⅄3Θn1 of (2⅄2Θn2/2⅄2Θn1)=(0.415/0)=0
1⅄4Θn1 from 1⅄3Θn2 of (2⅄2Θn3/2⅄2Θn2)/1⅄3Θn1 of (2⅄2Θn2/2⅄2Θn1)=(0.415/0)=0
1⅄4Θn2 from 1⅄3Θn3 of (2⅄2Θn4/2⅄2Θn3)/1⅄3Θn2 of (2⅄2Θn3/2⅄2Θn2)=(1.2048192771084337349397590361445783132530/0.415)=2.903178980984177674553636231673682682537349397590361445783132530120481927710843
And so on for ∈1⅄4Θn that differs from ∈2⅄4Θn1 from [1⅄3Θn1 of (2⅄2Θn2/2⅄2Θn1)/1⅄3Θn2 of (2⅄2Θn3/2⅄2Θn2)]=(0.415/0)=0
while alternately ∈2⅄3Θn1 of (2⅄2Θn1/2⅄2Θn2)=(0/2)=0
2⅄3Θn1 of (2⅄2Θn1/2⅄2Θn2)=(0/2)=0
2⅄3Θn2 of (2⅄2Θn2/2⅄2Θn3)=(2/0.83)=2.4096385542168674698795180722891566265060 or 2.409638554216867469879518072289156626506024096385542168674698795180722891566265060
2⅄3Θn3 of (2⅄2Θn3/2⅄2Θn4)=(0.83/1)=0.83
2⅄3Θn4 of (2⅄2Θn4/2⅄2Θn5)=(1/0.96)=1.0416
2⅄3Θn5 of (2⅄2Θn5/2⅄2Θn6)=(0.96/1.015626)
2⅄3Θn6 of (2⅄2Θn6/2⅄2Θn7)=(1.015626/0.994082840236686390532544378698224852071005917159763313609467455621301775147928)
And so on for ∈2⅄3Θn1 of (2⅄2Θn1/2⅄2Θn2)
then ∈2⅄4Θn of (2⅄3Θn1 of (2⅄2Θn1/2⅄2Θn2)/2⅄3Θn2 of (2⅄2Θn2/2⅄2Θn3)=(0/2.4096385542168674698795180722891566265060)=0
and
∈2⅄4Θn of (2⅄3Θn1 of (2⅄2Θn1/2⅄2Θn2)/2⅄3Θn2 of (2⅄2Θn2/2⅄2Θn3) is not ∈1⅄4Θn1 from 1⅄3Θn2 of (2⅄2Θn3/2⅄2Θn2)/1⅄3Θn1 of (2⅄2Θn2/2⅄2Θn1)
Alternate Path of divide 3⅄ to 2Θ for 3⅄2Θncn from 1Θncn variables
3⅄2Θn=(1Θncn/1Θncn) and of cn variable cn variable change division functions
so
3⅄2Θn1=(1Θn1c/1Θn1c)=(0/1)/(0/1)=(0/0)=0
3⅄2Θn2=(1Θn2c/1Θn2c)=(1/1)/(1/1)=(1/1)=1
3⅄2Θn3=(1Θn3c/1Θn3c)=(1/2)/(1/2)=(0.5/0.5)=1
3⅄2Θn4=(1Θn4c/1Θn4c)=(2/3)/(2/3)=(0.6/0.6)=1
and 3⅄2Θn4=(1Θn4c/1Θn4c2)=(2/3)/(2/3)c2=(0.6/0.66)
and 3⅄2Θn4=(1Θn4c2/1Θn4c)=(2/3)c2/(2/3)=(0.66/0.6)
and 3⅄2Θn4=(1Θn4c2/1Θn4c2)=(2/3)c2/(2/3)c2=(0.66/0.66) and so on for cn variable stem cycle
3⅄2Θn5=(1Θn5c/1Θn5c)=(0.6/0.6)=1
3⅄2Θn6=(1Θn6c/1Θn6c)=(0.625/0.625)=1
3⅄2Θn7=(1Θn7c/1Θn7c)=(8/13)/(8/13)=(0.615384/0.615384)=1
and 3⅄2Θn7=(1Θn7c/1Θn7c2)=(8/13)/(8/13)c2=(0.615384/0.615384615384)
and 3⅄2Θn7=(1Θn7c2/1Θn7c)=(8/13)c2/(8/13)=(0.615384615384/0.615384)
and 3⅄2Θn7=(1Θn7c2/1Θn7c2)=(8/13)c2/(8/13)c2=(0.615384615384/0.615384615384) and so on for cn variable stem cycle
3⅄2Θn8=(1Θn8c/1Θn8c)=(13/21)/(13/21)=(0.619047/0.619047)=1
and 3⅄2Θn8=(1Θn8c/1Θn8c2)=(13/21)/(13/21)c2=(0.619047/0.619047619047)
and 3⅄2Θn8=(1Θn8c2/1Θn8c)=(13/21)c2/(13/21)=(0.619047619047/0.619047)
and 3⅄2Θn8=(1Θn8c2/1Θn8c2)=(13/21)c2/(13/21)c2=(0.619047619047/0.619047619047) and so on for cn variable stem cycle
3⅄2Θn9=(1Θn9c/1Θn9c)=(21/34)/(21/34)=(0.61764705882352941/0.61764705882352941)=1
and 3⅄2Θn9=(1Θn9c/1Θn9c2)=(21/34)/(21/34)c2=(0.61764705882352941/0.617647058823529411764705882352941)
and 3⅄2Θn9=(1Θn9c2/1Θn9c)=(21/34)c2/(21/34)=(0.617647058823529411764705882352941/0.61764705882352941)
and 3⅄2Θn9=(1Θn9c2/1Θn9c2)=(21/34)c2/(21/34)c2=(0.617647058823529411764705882352941/0.617647058823529411764705882352941) and so on for cn variable stem cycle
3⅄2Θn10=(1Θn10c/1Θn10c)=(34/55)/(34/55)=(0.618/0.618)=1
and 3⅄2Θn10=(1Θn10c/1Θn10c2)=(34/55)/(34/55)c2=(0.618/0.61818)
and 3⅄2Θn10=(1Θn10c2/1Θn10c)=(34/55)c2/(34/55)=(0.61818/0.618)
and 3⅄2Θn10=(1Θn10c2/1Θn10c2)=(34/55)c2/(34/55)c2=(0.61818/0.61818) and so on for cn variable stem cycle
3⅄2Θn11=(1Θn11c/1Θn11c)=(55/89)/(55/89)=(0.6179775280878651685393258764044943820224719101123595505/0.6179775280878651685393258764044943820224719101123595505)=1
and 3⅄2Θn11=(1Θn11c/1Θn11c2)=(55/89)/(55/89)c2=(0.6179775280878651685393258764044943820224719101123595505/0.61797752808786516853932587640449438202247191011235955056179775280878651685393258764044943820224719101123595505)
and 3⅄2Θn11=(1Θn11c2/1Θn11c)=(55/89)c2/(55/89)=(0.61797752808786516853932587640449438202247191011235955056179775280878651685393258764044943820224719101123595505/0.6179775280878651685393258764044943820224719101123595505)
and 3⅄2Θn11=(1Θn11c2/1Θn11c2)=(55/89)c2/(55/89)c2=(0.61797752808786516853932587640449438202247191011235955056179775280878651685393258764044943820224719101123595505/0.61797752808786516853932587640449438202247191011235955056179775280878651685393258764044943820224719101123595505) and so on for cn variable stem cycle
3⅄2Θn12=(1Θn12c/1Θn12c)=(89/144)/(89/144)=(0.61805/0.61805)=1
and 3⅄2Θn12=(1Θn12c/1Θn12c2)=(89/144)/(89/144)c2=(0.61805/0.618055)
and 3⅄2Θn12=(1Θn12c2/1Θn12c)=(89/144)c2/(89/144)=(0.618055/0.61805)
and 3⅄2Θn12=(1Θn12c2/1Θn12c2)=(89/144)c2/(89/144)c2=(0.618055/0.618055) and so on for cn variable stem cycle
3⅄2Θn13=(1Θn13c/1Θn13c)=(144/233)/(144/233)=(0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566/0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566)=1
and 3⅄2Θn13=(1Θn13c/1Θn13c2)=(144/233)/(144/233)c2=(0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566/0.61802575536480643776824034334763948497854077253220600858369098712446351931330472103004291845493562231759656654935622317596566)
and 3⅄2Θn13=(1Θn13c2/1Θn13c)=(144/233)c2/(144/233)=(0.61802575536480643776824034334763948497854077253220600858369098712446351931330472103004291845493562231759656654935622317596566/0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566)
and 3⅄2Θn13=(1Θn13c2/1Θn13c2)=(144/233)c2/(144/233)c2=(0.61802575536480643776824034334763948497854077253220600858369098712446351931330472103004291845493562231759656654935622317596566/0.61802575536480643776824034334763948497854077253220600858369098712446351931330472103004291845493562231759656654935622317596566) and so on for cn variable stem cycle
3⅄2Θn14=(1Θn14c/1Θn14c)=(233/377)/(233/377)=(0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257)=1
and 3⅄2Θn14=(1Θn14c/1Θn14c2)=(233/377)/(233/377)=(0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257)
and 3⅄2Θn14=(1Θn14c2/1Θn14c)=(233/377)/(233/377)=(0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257)
and 3⅄2Θn14=(1Θn14c2/1Θn14c2)=(233/377)c2/(233/377)c2=(0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257) and so on for cn variable stem cycle
3⅄2Θn15=(1Θn15c/1Θn15c)=(377/610)/(377/610)=(0.618032786885245901639344262295081967213114754098360655737749/0.618032786885245901639344262295081967213114754098360655737749)=1
and 3⅄2Θn15=(1Θn15c/1Θn15c2)=(377/610)/(377/610)c2=(0.618032786885245901639344262295081967213114754098360655737749/0.61803278688524590163934426229508196721311475409836065573774918032786885245901639344262295081967213114754098360655737749)
and 3⅄2Θn15=(1Θn15c2/1Θn15c)=(377/610)c2/(377/610)=(0.61803278688524590163934426229508196721311475409836065573774918032786885245901639344262295081967213114754098360655737749/0.618032786885245901639344262295081967213114754098360655737749)
and 3⅄2Θn15=(1Θn15c2/1Θn15c2)=(377/610)c2/(377/610)c2=(0.61803278688524590163934426229508196721311475409836065573774918032786885245901639344262295081967213114754098360655737749/0.61803278688524590163934426229508196721311475409836065573774918032786885245901639344262295081967213114754098360655737749) and so on for cn variable stem cycle
and so on for function path of variables 3⅄2Θn
With variables factored for 1Θn and 2Θn now Path sets of 3Θ functions are
1⅄3Θn of 1⅄2Θn=(1⅄2Θn2cn/1⅄2Θn1cn)
2⅄3Θn of 1⅄2Θn=(1⅄2Θn1cn/1⅄2Θn2cn)
3⅄3Θn of 1⅄2Θn=(1⅄2Θn1cn/1⅄2Θn1cn)
1⅄3Θn of 2⅄2Θn=(2⅄2Θn2cn/2⅄2Θn1cn)
2⅄3Θn of 2⅄2Θn=(2⅄2Θn1cn/2⅄2Θn2cn)
3⅄3Θn of 2⅄2Θn=(2⅄2Θn1cn/2⅄2Θn1cn)
1⅄3Θn of 3⅄2Θn=(3⅄2Θn2cn/3⅄2Θn1cn)
2⅄3Θn of 3⅄2Θn=(3⅄2Θn1cn/3⅄2Θn2cn)
3⅄3Θn of 3⅄2Θn=(3⅄2Θn1cn/3⅄2Θn1cn)
Base Set Examples 1⅄3Θn1 of 1⅄2Θn
1⅄3Θn1 of 1⅄2Θn=(1⅄2Θn2cn/1⅄2Θn1cn)=(0.5/0)
1⅄3Θn2 of 1⅄2Θn=(1⅄2Θn3cn/1⅄2Θn2cn)=[(2/3)/(1/2)]/[(1/2)/(1/1)]=(1.2/0.5)
and 1⅄2Θn3=(1Θn4c2/1Θn3)=(2/3)/(1/2)=(0.66/0.5)=1.32
then 1⅄3Θn2 of 1⅄2Θn=(1⅄2Θn3cn/1⅄2Θn2cn)=(1.32/0.5) of 1Θn4c2 of 1⅄2Θn3cn base variant
1⅄3Θn3 of 1⅄2Θn=(1⅄2Θn4cn/1⅄2Θn3cn)=(1/1.2) or (1/1.32) or (1/1.332) or (0.09/1.2) or (0.09/1.32) or (0.09/1.332) or (0.009/1.2) or (0.009/1.32) or (0.009/1.332) and so on for variant base of cn at1Θn variables foctoring stem cycles.
1⅄3Θn4 of 1⅄2Θn=(1⅄2Θn5cn/1⅄2Θn4cn)=(1.0416/1) or (1.0416/0.09) or (1.0416/0.009) and so on for cn variants
1⅄3Θn5 of 1⅄2Θn=(1⅄2Θn6cn/1⅄2Θn5cn)=(0.9878144/1.0416) or (0.9878153846144/1.0416) or (0.9878144/1.04166) or (0.9878153846144/1.04166) and so on for variant base of cn stem cycle
1⅄3Θn6 of 1⅄2Θn=(1⅄2Θn7cn/1⅄2Θn6cn)=(1.00595237770/0.9878144) or (1.00595237770/0.9878153846144) or (1.00595237770237770/0.9878144) or (1.00595237770237770/0.9878153846144) and so on for variant base of cn stem cycle
1⅄3Θn7 of 1⅄2Θn=(1⅄2Θn8cn/1⅄2Θn7cn)=(0.61764705882352941/0.619047)/(0.619047/0.615384)
1⅄3Θn8 of 1⅄2Θn=(1⅄2Θn9cn/1⅄2Θn8cn)=(0.618/0.61764705882352941)/(0.61764705882352941/0.619047)
1⅄3Θn9 of 1⅄2Θn=(1⅄2Θn10cn/1⅄2Θn9cn)=(0.6179775280878651685393258764044943820224719101123595505/0.618)/(0.618/0.61764705882352941)
1⅄3Θn10 of 1⅄2Θn=(1⅄2Θn11cn/1⅄2Θn10cn)=(0.61805/0.6179775280878651685393258764044943820224719101123595505)/(0.6179775280878651685393258764044943820224719101123595505/0.618)
1⅄3Θn11 of 1⅄2Θn=(1⅄2Θn12cn/1⅄2Θn11cn)=(0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566/0.61805)/(0.61805/0.6179775280878651685393258764044943820224719101123595505)
1⅄3Θn12 of 1⅄2Θn=(1⅄2Θn13cn/1⅄2Θn12cn)=(0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566)/(0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566/0.61805)
1⅄3Θn13 of 1⅄2Θn=(1⅄2Θn14cn/1⅄2Θn13cn)=(0.618032786885245901639344262295081967213114754098360655737749/0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257)/(0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566)
1⅄3Θn14 of 1⅄2Θn=(1⅄2Θn15cn/1⅄2Θn14cn)=(0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870/0.618032786885245901639344262295081967213114754098360655737749)/(0.618032786885245901639344262295081967213114754098360655737749/0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257)
1⅄3Θn15 of 1⅄2Θn=(1⅄2Θn16cn/1⅄2Θn15cn)=(0.61670569685597996229805886023168309329993738259236054477144644896/0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870)/(0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870/0.618032786885245901639344262295081967213114754098360655737749)
Continued base chain ratios abbreviated
1⅄3Θn16 of 1⅄2Θn=(1⅄2Θn17cn/1⅄2Θn16cn)=[(1597/2584)/(987/1597)] / [(987/1597)/(610/987)]
1⅄3Θn17 of 1⅄2Θn=(1⅄2Θn18cn/1⅄2Θn17cn)=[(2584/4181)/(1597/2584)] / [(1597/2584)/(987/1597)]
1⅄3Θn18 of 1⅄2Θn=(1⅄2Θn19cn/1⅄2Θn18cn)=[(4181/6765)/(2584/4181)] / [(2584/4181)/(1597/2584)]
1⅄3Θn19 of 1⅄2Θn=(1⅄2Θn20cn/1⅄2Θn19cn)=[(6765/10946)/(4181/6765)] / [(4181/6765)/(2584/4181)]
1⅄3Θn20 of 1⅄2Θn=(1⅄2Θn21cn/1⅄2Θn20cn)=[(10946/17711)/(6765/10946)] / [(6765/10946)/(4181/6765)]
Base Set Examples 2⅄3Θn of 1⅄2Θn
2⅄3Θn1 of 1⅄2Θn=(1⅄2Θn1cn/1⅄2Θn2cn)=(0/1)
2⅄3Θn2 of 1⅄2Θn=(1⅄2Θn2cn/1⅄2Θn3cn)=(1/0.5)
2⅄3Θn3 of 1⅄2Θn=(1⅄2Θn3cn/1⅄2Θn4cn)=(0.5/0.6)
2⅄3Θn4 of 1⅄2Θn=(1⅄2Θn4cn/1⅄2Θn5cn)=(0.6/0.6)
2⅄3Θn5 of 1⅄2Θn=(1⅄2Θn5cn/1⅄2Θn6cn)=(0.6/0.625)
2⅄3Θn6 of 1⅄2Θn=(1⅄2Θn6cn/1⅄2Θn7cn)=(0.625/0.615384)
2⅄3Θn7 of 1⅄2Θn=(1⅄2Θn7cn/1⅄2Θn8cn)=(0.615384/0.619047)
2⅄3Θn8 of 1⅄2Θn=(1⅄2Θn8cn/1⅄2Θn9cn)=(0.619047/0.61764705882352941)
2⅄3Θn9 of 1⅄2Θn=(1⅄2Θn9cn/1⅄2Θn10cn)=(0.61764705882352941/0.618)
2⅄3Θn10 of 1⅄2Θn=(1⅄2Θn10cn/1⅄2Θn11cn)=(0.618/0.6179775280878651685393258764044943820224719101123595505)
2⅄3Θn11 of 1⅄2Θn=(1⅄2Θn11cn/1⅄2Θn12cn)=(0.6179775280878651685393258764044943820224719101123595505/0.61805)
2⅄3Θn12 of 1⅄2Θn=(1⅄2Θn12cn/1⅄2Θn13cn)=(0.61805/0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566)
2⅄3Θn13 of 1⅄2Θn=(1⅄2Θn13cn/1⅄2Θn14cn)=(0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566/0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257)
2⅄3Θn14 of 1⅄2Θn=(1⅄2Θn14cn/1⅄2Θn15cn)=(0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/0.618032786885245901639344262295081967213114754098360655737749)
2⅄3Θn15 of 1⅄2Θn=(1⅄2Θn15cn/1⅄2Θn16cn)=(0.618032786885245901639344262295081967213114754098360655737749/0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870)
and so on for variables 2⅄3Θn15 of 1⅄2Θn
Phi Theta Θ φ Q scale set paths and functions of cn stem cycle cell groups from y and p bases
123⅄ncn|Θ/Y|ncn 123⅄ncn|Y/Θ|ncn 123⅄ncn|YxΘ|ncn 123⅄ncn|Y+Θ|ncn 123⅄ncn|Y-Θ|ncn 123⅄ncn|Θ-Y|ncn
123⅄ncn|Θ/φ|ncn 123⅄ncn|φ/Θ|ncn 123⅄ncn|φxΘ|ncn 123⅄ncn|φ+Θ|ncn 123⅄ncn|φ-Θ|ncn 123⅄ncn|φ-Θ|ncn
123⅄ncn|Θ/P|ncn 123⅄ncn|P/Θ|ncn 123⅄ncn|PxΘ|ncn 123⅄ncn|P+Θ|ncn 123⅄ncn|P-Θ|ncn 123⅄ncn|Θ-P|ncn
123⅄ncn|Θ/Q|ncn 123⅄ncn|Q/Θ|ncn 123⅄ncn|QxΘ|ncn 123⅄ncn|Q+Θ|ncn 123⅄ncn|Q-Θ|ncn 123⅄ncn|Θ-Q|ncn
Phi Prime Theta Ratio sets of y p base variables
123⅄ncn|A/Θn|ncn 123⅄ncn|Θn/A|ncn
123⅄ncn|M/Θn|ncn 123⅄ncn|Θn/M|ncn
123⅄ncn|V/Θn|ncn 123⅄ncn|Θn/V|ncn
123⅄ncn|W/Θn|ncn 123⅄ncn|Θn/W|ncn
123⅄ncn|ᐱ/Θn|ncn 123⅄ncn|Θn/ᐱ|ncn
123⅄ncn|ᗑ/Θn|ncn 123⅄ncn|Θn/ᗑ|ncn
Theta Phi Divide of Y variable base
∈|(Θ)/φ|→→{2⅄yn/1⅄yn]=2⅄(Yn1/Yn2)/1⅄(Yn2/Yn1)
Θ/φn1=(Θn1/φn1)=2⅄(Yn1/Yn2)/1⅄(Yn2/Yn1)=(0/1)/(1/0)=(0)/(0)=0
Θ/φn2=(Θn2/φn2)=2⅄(Yn2/Yn3)/1⅄(Yn3/Yn2)=(1/1)/(1/1)=(1)/(1)=1
Θ/φn3=(Θn3/φn3)=2⅄(Yn3/Yn4)/1⅄(Yn4/Yn3)=(1/2)/(2/1)=(0.5)/(2)=0.25
Θ/φn4=(Θn4/φn4)=2⅄(Yn4/Yn5)/1⅄(Yn5/Yn4)=(2/3)/(3/2)=(0.6)/(1.5)=0.4 and Θ/φn4=(Θn4c2/φn4)=(0.66)/(1.5)=0.44 and so on for cn
Θ/φn5=(Θn5/φn5)=2⅄(Yn5/Yn6)/1⅄(Yn6/Yn5)=(3/5)/(5/3)=(0.6)/(1.6)=0.375 and Θ/φn5=(Θn5/φn5c2)=(0.6)/(1.66)=0.3614457831325301204819277108433734939759 and so on for cn
Θ/φn6=(Θn6/φn6)=(0.625/1.6)=0.390625 and neither variable Θn6 or φn6 have a factor of potential change of cn
Θ/φn7=(Θn7/φn7)=(0.615385/1.625)=0.3786984615384
Θ/φn8=(Θn8/φn8)=(0.619047/1.615384)
Θ/φn9=(Θn9/φn9)=(0.61764705882352941/1.619047)
Θ/φn10=(Θn10/φn10)=(0.618/1.61762941)
and so on for Θ/φn=(Θn/φn) that differ from 1⅄Θ/φn=(Θn2/φn1) and 2⅄Θ/φn=(Θn1/φn2) and 3⅄Θ/φn=(Θncn/φncn)
Phi Theta Divide of Y variable base
∈|φ/(Θ)|→→{1⅄yn/2⅄yn]=1⅄(Yn2/Yn1)/2⅄(Yn1/Yn2)
then Θ/φ and φ/Θ are basic function definitions that differ from variable example equations such as
1⅄Θn1/2⅄φn1
2⅄Θn1/1⅄φn1
3⅄Θn1/3⅄φn1
1⅄Θn2/2⅄φn2
2⅄Θn2/1⅄φn2
3⅄Θn2/3⅄φn2
1⅄φn1/1⅄Θn1
2⅄φn1/2⅄Θn1
3⅄φn1/3⅄Θn1
Equations can be as precise as (1⅄3Θn of 2⅄2Θn=(2⅄2Θn2cn/2⅄2Θn1cn))/1⅄6φn2
or 1⅄6φn2/(1⅄3Θn of 2⅄2Θn=(2⅄2Θn2cn/2⅄2Θn1cn)) to the stem cycle degree defined in cn specifics of the equation example when decimal limits of a calculating device are not limited to 10 digit roundings or limited in general.
Prime consecutive step tier base rationals of 2:199 of the 10 digit prime 1,000,000,007
1st tier 46 primes example 10 tiers to 9 divisions of primes with primes (p) or (P) P→Q→∈2⅄Q ∈1⅄Q
∈3⅄Q does not exist where numbers of p have no decimals path variant of cn
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199
2nd tier 1st divide
Path of Q base ∈1⅄Q
examples of ∈1⅄1Qn1=(pn2/pn1)
∈1⅄1Qn1 prime consecutive later divided by previous cycles back in remainder back to the first division remainder.
have not read this anywhere . . . this may help with the mersenne prime search of primes.
if 1⅄P=(pn2/pn1)=1⅄1Qn1 consecutive prime later divided by previous cycles back in remainder back to the first remainder then the prime no matter the number of digits when later prime divided by the next previous of consecutive primes will cycle back to the first remainder. The first 45 variables of 1⅄P=(pn2/pn1)=1⅄1Qn1 prove that fact. Both 2⅄P=(pn1/pn2)=2⅄1Qn equation combined with 1⅄P=(pn2/pn1)=1⅄1Qn1 equation can varify as functions of P with Q bases if primes are consecutive no matter the number of digits to the prime numbers.
1⅄1Qn1=(pn2/pn1)=(3/2)=1.5
1⅄1Qn2=(pn3/pn2)=(5/3)=1.6
1⅄1Qn3=(pn4/pn3)=(7/5)=1.4
1⅄1Qn4=(pn5/pn4)=(11/7)=1.571428
1⅄1Qn5=(pn6/pn5)=(13/11)=1.18
1⅄1Qn6=(pn7/pn6)=(17/13)=1.307692
1⅄1Qn7=(pn8/pn7)=(19/17)=1.1176470588235294
1⅄1Qn8=(pn9/pn8)=(23/19)=1.210526315789473684
1⅄1Qn9=(pn10/pn9)=(29/23)=1.2608695652173913043478
1⅄1Qn10=(pn11/pn10)=(31/29)=1.0689655172413793103448275862
1⅄1Qn11=(pn/pn)=(37/31)=1.193548387096774
1⅄1Qn12=(pn/pn)=(41/37)=1.108
1⅄1Qn13=(pn/pn)=(43/41)=1.04878
1⅄1Qn14=(pn/pn)=(47/43)=1.093023255813953488372
1⅄1Qn15=(pn/pn)=(53/47)=1.12765957446808510638297872340425531914893610702
1⅄1Qn16=(pn/pn)=(59/53)=1.1132075471698
1⅄1Qn17=(pn/pn)=(61/59)=1.0338983050847457627118644067796610169491525423728813559322
1⅄1Qn18=(pn/pn)=(67/61)=1.098360655737704918032786885245901639344262295081967213114754
1⅄1Qn19=(pn/pn)=(71/67)=1.059701492537313432835820895522388
1⅄1Qn20=(pn/pn)=(73/71)=1.02816901408450704225352112676056338
1⅄1Qn21=(pn/pn)=(79/73)=1.08219178
1⅄1Qn22=(pn/pn)=(83/79)=1.0506329113924
1⅄1Qn23=(pn/pn)=(89/83)=1.07228915662650602409638554216867469879518
1⅄1Qn24=(pn/pn)=(97/89)=1.08988764044943820224719101123595505617977528
1⅄1Qn25=(pn/pn)=(101/97)=1.04123092783505154639175257731958762886597938144329896907216494845360820618
1⅄1Qn26=(pn/pn)=(103/101)=1.0198
1⅄1Qn27=(pn/pn)=(107/103)=1.0388349514563106796111662136504854368932
1⅄1Qn28=(pn/pn)=(109/107)=1.01869158878504672897196261682242990654205607476635514
1⅄1Qn29=(pn/pn)=(113/109)=1.0366972477064220183486238532110091743119266055045871559633027522935779816513758712844
1⅄1Qn30=(pn/pn)=(127/113)=1.123893805308849557522
1⅄1Qn31=(pn/pn)=(131/127)=1.031496062992125984251968503937007874015748
1⅄1Qn32=(pn/pn)=(137/131)=1.045801526717557251908396946564885496183206106870229007633587786259541984732824427480916030534351145038167938931297099236641221374
1⅄1Qn33=(pn/pn)=(139/137)=1.01459854
1⅄1Qn34=(pn/pn)=(149/139)=1.071942446043165474820143884892086330935251798561151080291955395683453237410
1⅄1Qn35=(pn/pn)=(151/149)=1.01343624295302
1⅄1Qn36=(pn/pn)=(157/151)=1.0397350993377483443708609271523178807284768211920529801324503311258278145695364238410596026490066225165562913907218543046357615894
1⅄1Qn37=(pn/pn)=(163/157)=1.038216560509554140127388535031847133757961783439490445859872611464968152866242
1⅄1Qn38=(pn/pn)=(167/163)=1.024539877300613496932515337423312883435582822085889570552147239263803680981595092
1⅄1Qn39=(pn/pn)=(173/167)=1.0359281437125748502994011976047904191616766467065868263473053892215568862275449101796407185628742514970059880239520958083832335329341317365269461077844311377245508982
1⅄1Qn40=(pn/pn)=(179/173)=1.034682080924554913294797687861271676300578
1⅄1Qn41=(pn/pn)=(181/179)=1.0111731843575418994413407821229050279329608936536312849162
1⅄1Qn42=(pn/pn)=(191/181)=1.005524861878453038674033149171270718232044198895027624309392265193370165745856353591160220994475138121546961325966850828729281767955801104972375690607734806629834254143646408839779
1⅄1Qn43=(pn/pn)=(193/191)=1.01047120418848167539267015706806282722513089005235602094240837696335078534031413612565445026178
1⅄1Qn44=(pn/pn)=(197/193)=1.02072538860103626943005181347150259067357512953367875647668393782383419689119170984455958549222797927461139896373069948186528497409326424870466321243523316062176165803108808290155440414507772
1⅄1Qn45=(pn/pn)=(199/197)=1.01015228426395939086294416243654822335025380710659898477157360406091370558375634517766497461928934
Prime consecutive step tier base rationals of 2:199 of the 10 digit prime 1,000,000,007
1st tier 46 primes example 10 tiers to 9 divisions of primes with primes (p) or (P) P→Q→∈2⅄Q ∈1⅄Q
∈3⅄Q does not exist where numbers of p have no decimals path variant of cn
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199
2nd tier 1st divide
Alternate path P→Q→∈2⅄1Qn1=(pn1/pn2)
∈2⅄1 prime consecutive previous divided by later cycles back in remainder back to the dividend.
have not read this anywhere . . . this may help with the mersenne prime search of primes.
if 2⅄P=(pn1/pn2)=2⅄1Qn1 consecutive prime previous divided by later cycles back in remainder back to the dividend then the prime no matter the number of digits when previous prime divided by the next later consecutive prime will cycle back to the dividend. The first 45 variables of 2⅄P=(pn1/pn2)=2⅄1Qn prove that fact.
2⅄1Qn1=(pn1/pn2)=(2/3)=0.6
2⅄1Qn2=(pn2/pn3)=(3/5)=0.6
2⅄1Qn3=(pn3/pn4)=(5/7)=0.714285
2⅄1Qn4=(pn4/pn5)=(7/11)=0.63
2⅄1Qn5=(pn5/pn6)=(11/13)=0.846153
2⅄1Qn6=(pn6/pn7)=(13/17)=0.7647058823529411
2⅄1Qn7=(pn7/pn8)=(17/19)=0.894736842105263157
2⅄1Qn8=(pn8/pn9)=(19/23)=0.8260869565217391304347
2⅄1Qn9=(pn9/pn10)=(23/29)=0.7931034482758620689655172413
2⅄1Qn10=(pn10/pn11)=(29/31)=0.935483870967741
2⅄1Qn11=(pn11/pn12)=(31/37)=0.837
2⅄1Qn12=(pn12/pn13)=(37/41)=0.9024390243
2⅄1Qn13=(pn13/pn14)=(41/43)=0.953488372093023255813
2⅄1Qn14=(pn14/pn15)=(43/47)=0.9148936170212765957446808510638297872340425531
2⅄1Qn15=(pn15/pn16)=(47/53)=0.88679245283018867924528301
2⅄1Qn16=(pn16/pn17)=(53/59)=0.8983050847457627118644067796610169491525423728813559322033
2⅄1Qn17=(pn17/pn18)=(59/61)=0.967213114754098360655737704918032786885245901639344262295081
2⅄1Qn18=(pn18/pn19)=(61/67)=0.910447761194029850746268656716417
2⅄1Qn19=(pn19/pn20)=(67/71)=0.94366197183098591549295774647887323
2⅄1Qn20=(pn20/pn21)=(71/73)=0.97260273
2⅄1Qn21=(pn21/pn22)=(73/79)=0.9240506329113
2⅄1Qn22=(pn22/pn23)=(79/83)=0.95180722891566265060240963855421686746987
2⅄1Qn23=(pn23/pn24)=(83/89)=0.93258426966292134831460674157303370786516853
2⅄1Qn24=(pn24/pn25)=(89/97)=0.917525773195876288659793814432989690721649484536082474226804123711340206185567010309278350515463
2⅄1Qn25=(pn25/pn26)=(97/101)=0.9603
2⅄1Qn26=(pn26/pn27)=(101/103)=0.9805825242718446601941747572815533
2⅄1Qn27=(pn27/pn28)=(103/107)=0.96261682242990654205607476635514018691588785046728971
2⅄1Qn28=(pn28/pn29)=(107/109)=0.0981651376146788990825688073394495412844036697247706422018348623853211009174311926605504587155963302752293577
2⅄1Qn29=(pn29/pn30)=(109/113)=0.9646017699115044247787610619469026548672566371681415929203539823008849557522123893805309734513274336283185840707
2⅄1Qn30=(pn30/pn31)=(113/127)=0.88976377952755905511811023622047244094481
2⅄1Qn31=(pn31/pn32)=(127/131)=0.969465648854961832061068015267175572519083
2⅄1Qn32=(pn32/pn33)=(131/137)=0.95620437
2⅄1Qn33=(pn33/pn34)=(137/139)=0.9856115107913669064748201438848920863309352517
2⅄1Qn34=(pn34/pn35)=(139/149)=0.932885906040268456375838926174496651006711409395973154362416107382550335570469798657718120805369127516778523489
2⅄1Qn35=(pn35/pn36)=(149/151)=0.986754966887417218543046357615894039735099337748344370860927152317880794701
2⅄1Qn36=(pn36/pn37)=(151/157)=0.961783439490445859872611464968152866242038216560509554140127388535031847133757
2⅄1Qn37=(pn37/pn38)=(157/163)=0.963190184049079754601226993865030674846625766871165644171779141104294478527607361
2⅄1Qn38=(pn38/pn39)=(163/167)=0.9760479041916167664670658682634730538922155688622754491017964071856287425149700598802395209580838323353293413173652694610778443113772455089820359281437125748502994011
2⅄1Qn39=(pn39/pn40)=(167/173)=0.9653179190751445086705202312138728323699421
2⅄1Qn40=(pn40/pn41)=(173/179)=0.96648044692737430167597765363128491620111731843575418994413407821229050279329608938547486033519553072625698324022346336871508379888268156424581005586592178770949720670391061452513
2⅄1Qn41=(pn41/pn42)=(179/181)=0.9889502762430939226519337016574585635359116022099447513812154696132596685082877292817679558011049723756906077348066298342541436464088397790055248618784530386740331491712707182320441
2⅄1Qn42=(pn42/pn43)=(181/191)=0.94764397905759162303664921465968586387434554973821989528795811518324607329842931937172774869109
2⅄1Qn43=(pn43/pn44)=(191/193)=0.989637304699481864284974093264248704663212435233160621761658031088082901554404145077720207253886010362694300518134715025906735751295336787564766839378238341917098445595854922279792746113
2⅄1Qn44=(pn44/pn45)=(193/197)=0.979695431
2⅄1Qn45=(pn45/pn46)=(197/199)=0.989949748743718592964824120603015075025125628140703517587939698492462311557763819095477386934673366834170854271356783919597
3rd tier 2nd Prime 1⅄(2⅄1Q) base
Variants ∈ next set of prime radical decimal stem path factoring to the degree of the variant decimal cycles per array.
Quadratic equations dependent of 4 prime radicals decimal cycle limit or break in stem numeral factoring.
Factoring for variables of ∈2Qnc1 and so on →. . .
∈(Qn2/Qn1c1)=(0.6/0.6)=1
∈2Qn1=1
Variant prime radical divide
∈(Qn2/Qn1c2)=0.6/0.66=0.909
(Qn2/Qn1c3)=0.6/0.666=0.9009 and so on →. . .
then
∈(Qn3c1/Qn2)=0.714285/0.6=1.190475
∈2Qn2=1.190475
(Qn3c2/Qn2)=0.714285714285/0.6=1.19047595238083 and so on →. . .
then
∈(Qn4c1/Qn3c1)=0.63/0.714285=0.8819994 and so on →. . .
∈2Qn3=0.8819994
∈(Qn5c1/Qn4c1)=0.846153/0.63=1.3431
∈2Qn4=1.3431
∈(Qn6c1/Qn5c1)=0.7647058823529411/0.846153=0.9037442192^522405
∈2Qn5=0.9037442192522405
and so on →. . .
1⅄2Q divide starting at 1⅄(Qn2/Qn1) then 2⅄2Q divide starting at 2⅄(Qn1/Qn2)
WHILE
in short 1(Qn2/Qn1) is not 2(Qn1/Qn2)
1⅄(1⅄2Q)n1=(1⅄1Q)n2/(1⅄1Q)n1 is not 2⅄(1⅄2Q)n2=(1⅄1Q)n1/(1⅄1Q)n2
4th tier 3rd Prime 1⅄(1⅄(2⅄1Q) base
Variants ∈ next set of prime radical decimal stem path factoring to the degree of the variant decimal cycles per array.
Quadratic equations dependent of 4 prime radicals decimal cycle limit or break in stem numeral factoring.
Factoring for variables of ∈3Qnc1 and so on →. . .
∈{(Qn4/Qn3)/(Qn2/Qn1)}=2Qn2/2Qn1=0.9/1=0.9
∈3Qn1=0.9
then {(Qn4/Qn3)c2/(Qn2/Qn1)}=2Qn2c2/2Qn1=0.909/1=0.909 and so on →. . . where c2 is applicable to {(Qn4/Qn3)c2
∈{(Qn5/Qn4)/(Qn3/Qn2)}=2Qn3/2Qn2=1.190475/0.9=1.32275
∈3Qn2=1.32275
then {(Qn5/Qn4)/(Qn3/Qn2)c2}=2Qn3/2Qn2c2=1.190475/0.909=1.2106435 and so on →. . .
∈{(Qn6/Qn5)/(Qn4/Qn3)}=2Qn4/2Qn3=0.8819994/1.190475=0.740880236
∈3Qn3=0.740880236
then {(Qn6/Qn5)c2/(Qn4/Qn3)}=2Qn4c2/2Qn3=0.8819994819994/1.190475=0.740880305759801 and so on →. . .
5th tier 4th Prime 1⅄(1⅄(1⅄(2⅄1Q) base
Variants ∈ next set of prime radical decimal stem path factoring to the degree of the variant decimal cycles per array.
Quadratic equations dependent of 4 prime radicals decimal cycle limit or break in stem numeral factoring.
Factoring for variables of ∈4Qnc1 and so on →. . .
∈(3Qn2/3Qn1)=1.4679
4Qn1=1.4679
then ∈(3Qn2/3Qn1c2)=1.45517
∈(3Qn3/3Qn2)=0.560106018522
4Qn2=0.560106018522
then ∈(3Qn3c2/3Qn2)=0.560106019187477603 and so on . . .
6th tier 5th Prime 1⅄(1⅄(1⅄(1⅄(2⅄1Q) base
Variants ∈ next set of prime radical decimal stem path factoring to the degree of the variant decimal cycles per array.
Quadratic equations dependent of 4 prime radicals decimal cycle limit or break in stem numeral factoring.
Factoring for variables of ∈5Qnc1 and so on →. . .
∈(3Qn3/3Qn2)/(3Qn2/3Qn1)=(4Qn2/4Qn1)=(0.560106018522/1.4679)
∈5Qn1=0.381569601827099938687921520539546290619251992642550582464745554874446488180393759792901423802711356359418219905988147011376796784522106410518427768580966005858709721370665576674160365147489611008924313645343688262147285237413946522242659581715375706792015848913413720280673070372641188091831868655902990666939164793242046460930376728659990625655698617072007629947544110634239389604196477961714013216591389059200279985012603038354111315484703998910007629947544110634239389604196471149260848831664282308059132093466857415355269432522651406771578445398187887458273724368144969003337102050548402479732951835956809046937802302609160956195926153007698072071667007745827372436814496900333810205054
⅄Q Alternate Base Path Variants 2nd tier of Q and third divide of P prime base quotient ratios
L=∈1⅄(1⅄Qn2/2⅄Qn1)cn
K=∈2⅄(1⅄Qn1/2⅄Qn2)cn
U=∈1⅄(2⅄Qn2/1⅄Qn1)cn
J=∈2⅄(2⅄Qn1/1⅄Qn2)cn
However, ∈1⅄2Q varies to the degree of Q path 1⅄ and 2⅄ and differ entirely from ∈L, ∈K, ∈U, and ∈J
1⅄2Q=(Nn2cn/Nn1cn) and N is Q of path 1⅄ or 2⅄ paths of divided consecutive Primes P.
So ∈1⅄2Q=[1⅄(1⅄2Q)=(1⅄Qn2cn/1⅄Qn1cn)] and ∈1⅄2Q=[1⅄(2⅄2Q)=(2⅄Qn2cn/2⅄Qn1cn)] if ∈1⅄2Q=(Nn2cn/Nn1cn)
Then
1⅄(1⅄2Q)n1=[1⅄2Q=(1⅄Qn2c1/1⅄Qn1c1)]=(1.6/1.5)=1.06
1⅄(1⅄2Q)n2=[1⅄2Q=(1⅄Qn3c1/1⅄Qn2c1)]=(1.4/1.6)=0.875
1⅄(1⅄2Q)n3=[1⅄2Q=(1⅄Qn4c1/1⅄Qn3c1)]=(1.571428/1.4)=1.12244857142
1⅄(1⅄2Q)n4=[1⅄2Q=(1⅄Qn5c1/1⅄Qn4c1)]=(1.18/1.571428)
1⅄(1⅄2Q)n5=[1⅄2Q=(1⅄Qn6c1/1⅄Qn5c1)]=(1.307692/1.18)
1⅄(1⅄2Q)n6=[1⅄2Q=(1⅄Qn7c1/1⅄Qn6c1)]=(1.1176470588235294/1.307692)
1⅄(1⅄2Q)n7=[1⅄2Q=(1⅄Qn8c1/1⅄Qn7c1)]=(1.210526315789473684/1.1176470588235294)
1⅄(1⅄2Q)n8=[1⅄2Q=(1⅄Qn9c1/1⅄Qn8c1)]=(1.2608695652173913043478/1.210526315789473684)
1⅄(1⅄2Q)n9=[1⅄2Q=(1⅄Qn10c1/1⅄Qn9c1)]=(1.0689655172413793103448275862/1.2608695652173913043478)
1⅄(1⅄2Q)n10=[1⅄2Q=(1⅄Qn11c1/1⅄Qn10c1)]=(1.193548387096774/1.0689655172413793103448275862)
1⅄(1⅄2Q)n11=[1⅄2Q=(1⅄Qn12c1/1⅄Qn11c1)]=(1.108/1.193548387096774)
1⅄(1⅄2Q)n12=[1⅄2Q=(1⅄Qn13c1/1⅄Qn12c1)]=(1.04878/1.108)
1⅄(1⅄2Q)n13=[1⅄2Q=(1⅄Qn14c1/1⅄Qn13c1)]=(1.093023255813953488372/1.04878)
1⅄(1⅄2Q)n14=[1⅄2Q=(1⅄Qn15c1/1⅄Qn14c1)]=(1.12765957446808510638297872340425531914893610702/1.093023255813953488372)
1⅄(1⅄2Q)n15=[1⅄2Q=(1⅄Qn16c1/1⅄Qn15c1)]=(1.1132075471698/1.12765957446808510638297872340425531914893610702)
1⅄(1⅄2Q)n16=[1⅄2Q=(1⅄Qn17c1/1⅄Qn16c1)]=(1.0338983050847457627118644067796610169491525423728813559322/1.1132075471698)
1⅄(1⅄2Q)n17=[1⅄2Q=(1⅄Qn18c1/1⅄Qn17c1)]=(1.098360655737704918032786885245901639344262295081967213114754/1.0338983050847457627118644067796610169491525423728813559322)
1⅄(1⅄2Q)n18=[1⅄2Q=(1⅄Qn19c1/1⅄Qn18c1)]=(1.059701492537313432835820895522388/1.098360655737704918032786885245901639344262295081967213114754)
1⅄(1⅄2Q)n19=[1⅄2Q=(1⅄Qn20c1/1⅄Qn19c1)]=(1.02816901408450704225352112676056338/1.059701492537313432835820895522388)
1⅄(1⅄2Q)n20=[1⅄2Q=(1⅄Qn21c1/1⅄Qn20c1)]=(1.08219178/1.02816901408450704225352112676056338)
1⅄(1⅄2Q)n21=[1⅄2Q=(1⅄Qn22c1/1⅄Qn21c1)]=(1.0506329113924/1.08219178)
1⅄(1⅄2Q)n22=[1⅄2Q=(1⅄Qn23c1/1⅄Qn22c1)]=(1.07228915662650602409638554216867469879518/1.0506329113924)
1⅄(1⅄2Q)n23=[1⅄2Q=(1⅄Qn24c1/1⅄Qn23c1)]=(1.08988764044943820224719101123595505617977528/1.07228915662650602409638554216867469879518)
1⅄(1⅄2Q)n24=[1⅄2Q=(1⅄Qn25c1/1⅄Qn24c1)]=(1.04123092783505154639175257731958762886597938144329896907216494845360820618/1.08988764044943820224719101123595505617977528)
1⅄(1⅄2Q)n25=[1⅄2Q=(1⅄Qn26c1/1⅄Qn25c1)]=(1.0198/1.04123092783505154639175257731958762886597938144329896907216494845360820618)
1⅄(1⅄2Q)n26=[1⅄2Q=(1⅄Qn27c1/1⅄Qn26c1)]=(1.0388349514563106796111662136504854368932/1.0198)
1⅄(1⅄2Q)n27=[1⅄2Q=(1⅄Qn28c1/1⅄Qn27c1)]=(1.01869158878504672897196261682242990654205607476635514/1.0388349514563106796111662136504854368932)
1⅄(1⅄2Q)n28=[1⅄2Q=(1⅄Qn29c1/1⅄Qn28c1)]=(1.0366972477064220183486238532110091743119266055045871559633027522935779816513758712844/1.01869158878504672897196261682242990654205607476635514)
1⅄(1⅄2Q)n29=[1⅄2Q=(1⅄Qn30c1/1⅄Qn29c1)]=(1.123893805308849557522/1.0366972477064220183486238532110091743119266055045871559633027522935779816513758712844)
1⅄(1⅄2Q)n30=[1⅄2Q=(1⅄Qn31c1/1⅄Qn30c1)]=(1.031496062992125984251968503937007874015748/1.123893805308849557522)
1⅄(1⅄2Q)n31=[1⅄2Q=(1⅄Qn32c1/1⅄Qn31c1)]=(1.045801526717557251908396946564885496183206106870229007633587786259541984732824427480916030534351145038167938931297099236641221374/1.031496062992125984251968503937007874015748)
1⅄(1⅄2Q)n32=[1⅄2Q=(1⅄Qn33c1/1⅄Qn32c1)]=(1.01459854/1.045801526717557251908396946564885496183206106870229007633587786259541984732824427480916030534351145038167938931297099236641221374)
1⅄(1⅄2Q)n33=[1⅄2Q=(1⅄Qn34c1/1⅄Qn33c1)]=(1.071942446043165474820143884892086330935251798561151080291955395683453237410/1.01459854)
1⅄(1⅄2Q)n34=[1⅄2Q=(1⅄Qn35c1/1⅄Qn34c1)]=(1.01343624295302/1.071942446043165474820143884892086330935251798561151080291955395683453237410)
1⅄(1⅄2Q)n35=[1⅄2Q=(1⅄Qn36c1/1⅄Qn35c1)]=(1.0397350993377483443708609271523178807284768211920529801324503311258278145695364238410596026490066225165562913907218543046357615894/1.01343624295302)
1⅄(1⅄2Q)n36=[1⅄2Q=(1⅄Qn37c1/1⅄Qn36c1)]=(1.038216560509554140127388535031847133757961783439490445859872611464968152866242/1.0397350993377483443708609271523178807284768211920529801324503311258278145695364238410596026490066225165562913907218543046357615894)
1⅄(1⅄2Q)n37=[1⅄2Q=(1⅄Qn38c1/1⅄Qn37c1)]=(1.024539877300613496932515337423312883435582822085889570552147239263803680981595092/1.038216560509554140127388535031847133757961783439490445859872611464968152866242)
1⅄(1⅄2Q)n38=[1⅄2Q=(1⅄Qn39c1/1⅄Qn38c1)]=(1.0359281437125748502994011976047904191616766467065868263473053892215568862275449101796407185628742514970059880239520958083832335329341317365269461077844311377245508982/1.024539877300613496932515337423312883435582822085889570552147239263803680981595092)
1⅄(1⅄2Q)n39=[1⅄2Q=(1⅄Qn40c1/1⅄Qn39c1)]=(1.034682080924554913294797687861271676300578/1.0359281437125748502994011976047904191616766467065868263473053892215568862275449101796407185628742514970059880239520958083832335329341317365269461077844311377245508982)
1⅄(1⅄2Q)n40=[1⅄2Q=(1⅄Qn41c1/1⅄Qn40c1)]=(1.0111731843575418994413407821229050279329608936536312849162/1.034682080924554913294797687861271676300578)
1⅄(1⅄2Q)n41=[1⅄2Q=(1⅄Qn42c1/1⅄Qn41c1)]=(1.005524861878453038674033149171270718232044198895027624309392265193370165745856353591160220994475138121546961325966850828729281767955801104972375690607734806629834254143646408839779/1.0111731843575418994413407821229050279329608936536312849162)
1⅄(1⅄2Q)n42=[1⅄2Q=(1⅄Qn43c1/1⅄Qn42c1)]=(1.01047120418848167539267015706806282722513089005235602094240837696335078534031413612565445026178/1.005524861878453038674033149171270718232044198895027624309392265193370165745856353591160220994475138121546961325966850828729281767955801104972375690607734806629834254143646408839779)
1⅄(1⅄2Q)n43=[1⅄2Q=(1⅄Qn44c1/1⅄Qn43c1)]=(1.02072538860103626943005181347150259067357512953367875647668393782383419689119170984455958549222797927461139896373069948186528497409326424870466321243523316062176165803108808290155440414507772/1.01047120418848167539267015706806282722513089005235602094240837696335078534031413612565445026178)
1⅄(1⅄2Q)n44=[1⅄2Q=(1⅄Qn45c1/1⅄Qn44c1)]=(1.01015228426395939086294416243654822335025380710659898477157360406091370558375634517766497461928934/1.02072538860103626943005181347150259067357512953367875647668393782383419689119170984455958549222797927461139896373069948186528497409326424870466321243523316062176165803108808290155440414507772)
and so on for variables of ∈1⅄(1⅄2Q)n=[1⅄2Q=(1⅄Qn2cn/1⅄Qn1cn)] that vary to degrees of stem cycle count variant 1⅄(1⅄2Q)ncn
Functions applicable to variables of ∈1⅄(1⅄2Q)ncn=[1⅄2Q=(1⅄Qn2cn/1⅄Qn1cn)]
X⅄=(n2xn1) example X⅄(1⅄2Q)n=[X2Q=(1⅄Qn2cnx1⅄Qn1cn)]
+⅄=(nncn+nncn) example +⅄(1⅄2Q)n=[+⅄2Q=(1⅄Qn2cn+1⅄Qn1cn)]
1-⅄=(n2-n1) example 1-⅄(1⅄2Q)n=[1-⅄2Q=(1⅄Qn2cn-1⅄Qn1cn)]
3rd tier of Q and 4th divide of P prime base quotient ratios
Then example 1⅄(1⅄3Q)n1 of (1⅄2Qn2c1/1⅄2Qn1c1)] so
1⅄(1⅄3Q)n1 of (1⅄2Qn2c1/1⅄2Qn1c1)]=(0.875/1.06)=0.825471698113207
1⅄(1⅄3Q)n2 of (1⅄2Qn3c1/1⅄2Qn2c1)]=(1.12244857142/0.875)=1.28279836733714285
1⅄(1⅄3Q)n of (1⅄2Qn4c1/1⅄2Qn3c1)]=[(1⅄Qn5c1/1⅄Qn4c1)/(1⅄Qn4c1/1⅄Qn3c1)]=[(1.18/1.571428)/(1.571428/1.4)]
and so on for variables of ∈1⅄(1⅄3Q)ncn of (1⅄2Qn2c1/1⅄2Qn1c1)]
4th tier of Q and 5th divide of P prime base quotient ratios
Then example 1⅄(1⅄4Q)n1 of (1⅄3Qn2c1/1⅄3Qn1c1)] so
1⅄(1⅄4Q)n1 of (1⅄3Qn2c1/1⅄3Qn1c1)]=(1.28279836733714285/0.825471698113207)
1⅄(1⅄4Q)n1 of (1⅄3Qn2c1/1⅄3Qn1c1)]=[(1⅄2Qn4c1/1⅄2Qn3c1)/(1⅄2Qn3c1/1⅄2Qn2c1)]
and so on for variables of ∈1⅄(1⅄4Q)ncn of (1⅄3Qn2c1/1⅄3Qn1c1)]
Again ⅄Q Alternate Base Path Variants 2nd tier of Q and third divide of P prime base quotient ratios
if ∈1⅄2Q=[1⅄(1⅄2Q)=(1⅄Qn2cn/1⅄Qn1cn)] and ∈1⅄2Q=[1⅄(2⅄2Q)=(2⅄Qn2cn/2⅄Qn1cn)] if ∈1⅄2Q=(Nn2cn/Nn1cn)
Then ∈1⅄2Q=[1⅄(2⅄2Q)=(2⅄Qn2cn/2⅄Qn1cn)]=[(Pn2/Pn3)/(Pn1/Pn2)]=[(3/5)/(2/3)]=(0.6/0.^6)=1 if cn of 2⅄Qn1cn ia 1 stem decimal cycle for variable 2⅄Qn1c1
1⅄(1⅄2Q)n1=[1⅄2Q=(2⅄Qn2c1/2⅄Qn1c1)]=(0.6/0.6)=1
1⅄(1⅄2Q)n2=[1⅄2Q=(2⅄Qn3c1/2⅄Qn2c1)]=(0.714285/0.6)=1.190475
1⅄(1⅄2Q)n3=[1⅄2Q=(2⅄Qn4c1/2⅄Qn3c1)]=(0.63/0.714285)=0.882000
1⅄(1⅄2Q)n4=[1⅄2Q=(2⅄Qn5c1/2⅄Qn4c1)]=(0.846153/0.63)=1.3431
1⅄(1⅄2Q)n5=[1⅄2Q=(2⅄Qn6c1/2⅄Qn5c1)]=(0.7647058823529411/0.846153)=0.9037442192522405
1⅄(1⅄2Q)n6=[1⅄2Q=(2⅄Qn7c1/2⅄Qn6c1)]=(0.894736842105263157/0.7647058823529411)=1.170040485829959630
1⅄(1⅄2Q)n7=[1⅄2Q=(2⅄Qn8c1/2⅄Qn7c1)]=(0.8260869565217391304347/0.894736842105263157)=0.9232736572890025584679383631713554996444089514066496172914677749360613819973501278772378525855854219948849114091148337595907937620560102301790290561
1⅄(1⅄2Q)n8=[1⅄2Q=(2⅄Qn9c1/2⅄Qn8c1)]=(0.7931034482758620689655172413/0.8260869565217391304347)=0.960072595281306715063616878306896551724137940635199110707803992741431940963702359346642564246727949183303085309056251742286751361162484572542649727767695195825675317604355716888003620163339382940109852993595281306715063616878306896551724137940635199110707803992741431940963702359346642564246727949183303085309056251742286751361162484572542649727767695195825675317604355716888003620163339382940109852993
1⅄(1⅄2Q)n9=[1⅄2Q=(2⅄Qn10c1/2⅄Qn9c1)]=(0.935483870967741/0.7931034482758620689655172413)
1⅄(1⅄2Q)n10=[1⅄2Q=(2⅄Qn11c1/2⅄Qn10c1)]=(0.837/0.935483870967741)
1⅄(1⅄2Q)n11=[1⅄2Q=(2⅄Qn12c1/2⅄Qn11c1)]=(0.9024390243/0.837)
1⅄(1⅄2Q)n12=[1⅄2Q=(2⅄Qn13c1/2⅄Qn12c1)]=(0.953488372093023255813/0.9024390243)
1⅄(1⅄2Q)n13=[1⅄2Q=(2⅄Qn14c1/2⅄Qn13c1)]=(0.9148936170212765957446808510638297872340425531/0.953488372093023255813)
1⅄(1⅄2Q)n14=[1⅄2Q=(2⅄Qn15c1/2⅄Qn14c1)]=(0.88679245283018867924528301/0.9148936170212765957446808510638297872340425531)
1⅄(1⅄2Q)n15=[1⅄2Q=(2⅄Qn16c1/2⅄Qn15c1)]=(0.8983050847457627118644067796610169491525423728813559322033/0.88679245283018867924528301)
1⅄(1⅄2Q)n16=[1⅄2Q=(2⅄Qn17c1/2⅄Qn16c1)]=(0.967213114754098360655737704918032786885245901639344262295081/0.8983050847457627118644067796610169491525423728813559322033)
1⅄(1⅄2Q)n17=[1⅄2Q=(2⅄Qn18c1/2⅄Qn17c1)]=(0.910447761194029850746268656716417/0.967213114754098360655737704918032786885245901639344262295081)
1⅄(1⅄2Q)n18=[1⅄2Q=(2⅄Qn19c1/2⅄Qn18c1)]=(0.94366197183098591549295774647887323/0.910447761194029850746268656716417)
1⅄(1⅄2Q)n19=[1⅄2Q=(2⅄Qn20c1/2⅄Qn19c1)]=(0.97260273/0.94366197183098591549295774647887323)
1⅄(1⅄2Q)n20=[1⅄2Q=(2⅄Qn21c1/2⅄Qn20c1)]=(0.9240506329113/0.97260273)
1⅄(1⅄2Q)n21=[1⅄2Q=(2⅄Qn22c1/2⅄Qn21c1)]=(0.95180722891566265060240963855421686746987/0.9240506329113)
1⅄(1⅄2Q)n22=[1⅄2Q=(2⅄Qn23c1/2⅄Qn22c1)]=(0.93258426966292134831460674157303370786516853/0.95180722891566265060240963855421686746987)
1⅄(1⅄2Q)n23=[1⅄2Q=(2⅄Qn24c1/2⅄Qn23c1)]=(0.917525773195876288659793814432989690721649484536082474226804123711340206185567010309278350515463/0.93258426966292134831460674157303370786516853)
1⅄(1⅄2Q)n24=[1⅄2Q=(2⅄Qn25c1/2⅄Qn24c1)]=(0.9603/0.917525773195876288659793814432989690721649484536082474226804123711340206185567010309278350515463)
1⅄(1⅄2Q)n25=[1⅄2Q=(2⅄Qn26c1/2⅄Qn25c1)]=(0.9805825242718446601941747572815533/0.9603)
1⅄(1⅄2Q)n26=[1⅄2Q=(2⅄Qn27c1/2⅄Qn26c1)]=(0.96261682242990654205607476635514018691588785046728971/0.9805825242718446601941747572815533)
1⅄(1⅄2Q)n27=[1⅄2Q=(2⅄Qn28c1/2⅄Qn27c1)]=(0.0981651376146788990825688073394495412844036697247706422018348623853211009174311926605504587155963302752293577/0.96261682242990654205607476635514018691588785046728971)
1⅄(1⅄2Q)n28=[1⅄2Q=(2⅄Qn29c1/2⅄Qn28c1)]=(0.9646017699115044247787610619469026548672566371681415929203539823008849557522123893805309734513274336283185840707/0.0981651376146788990825688073394495412844036697247706422018348623853211009174311926605504587155963302752293577)
1⅄(1⅄2Q)n29=[1⅄2Q=(2⅄Qn30c1/2⅄Qn29c1)]=(0.88976377952755905511811023622047244094481/0.9646017699115044247787610619469026548672566371681415929203539823008849557522123893805309734513274336283185840707)
1⅄(1⅄2Q)n30=[1⅄2Q=(2⅄Qn31c1/2⅄Qn30c1)]=(0.969465648854961832061068015267175572519083/0.88976377952755905511811023622047244094481)
1⅄(1⅄2Q)n31=[1⅄2Q=(2⅄Qn32c1/2⅄Qn31c1)]=(0.95620437/0.969465648854961832061068015267175572519083)
1⅄(1⅄2Q)n32=[1⅄2Q=(2⅄Qn33c1/2⅄Qn32c1)]=(0.9856115107913669064748201438848920863309352517/0.95620437)
1⅄(1⅄2Q)n33=[1⅄2Q=(2⅄Qn34c1/2⅄Qn33c1)]=(0.932885906040268456375838926174496651006711409395973154362416107382550335570469798657718120805369127516778523489/0.9856115107913669064748201438848920863309352517)
1⅄(1⅄2Q)n34=[1⅄2Q=(1⅄Qn35c1/2⅄Qn34c1)]=(0.986754966887417218543046357615894039735099337748344370860927152317880794701/0.932885906040268456375838926174496651006711409395973154362416107382550335570469798657718120805369127516778523489)
1⅄(1⅄2Q)n35=[1⅄2Q=(2⅄Qn36c1/2⅄Qn35c1)]=(0.961783439490445859872611464968152866242038216560509554140127388535031847133757/0.986754966887417218543046357615894039735099337748344370860927152317880794701)
1⅄(1⅄2Q)n36=[1⅄2Q=(2⅄Qn37c1/2⅄Qn36c1)]=(0.963190184049079754601226993865030674846625766871165644171779141104294478527607361/0.961783439490445859872611464968152866242038216560509554140127388535031847133757)
1⅄(1⅄2Q)n37=[1⅄2Q=(2⅄Qn38c1/2⅄Qn37c1)]=(0.9760479041916167664670658682634730538922155688622754491017964071856287425149700598802395209580838323353293413173652694610778443113772455089820359281437125748502994011/0.963190184049079754601226993865030674846625766871165644171779141104294478527607361)
1⅄(1⅄2Q)n38=[1⅄2Q=(2⅄Qn39c1/2⅄Qn38c1)]=(0.9653179190751445086705202312138728323699421/0.9760479041916167664670658682634730538922155688622754491017964071856287425149700598802395209580838323353293413173652694610778443113772455089820359281437125748502994011)
1⅄(1⅄2Q)n39=[1⅄2Q=(2⅄Qn40c1/2⅄Qn39c1)]=(0.96648044692737430167597765363128491620111731843575418994413407821229050279329608938547486033519553072625698324022346336871508379888268156424581005586592178770949720670391061452513/0.9653179190751445086705202312138728323699421)
1⅄(1⅄2Q)n40=[1⅄2Q=(2⅄Qn41c1/2⅄Qn40c1)]=(0.9889502762430939226519337016574585635359116022099447513812154696132596685082877292817679558011049723756906077348066298342541436464088397790055248618784530386740331491712707182320441/0.96648044692737430167597765363128491620111731843575418994413407821229050279329608938547486033519553072625698324022346336871508379888268156424581005586592178770949720670391061452513)
1⅄(1⅄2Q)n41=[1⅄2Q=(2⅄Qn42c1/2⅄Qn41c1)]=(0.94764397905759162303664921465968586387434554973821989528795811518324607329842931937172774869109/0.9889502762430939226519337016574585635359116022099447513812154696132596685082877292817679558011049723756906077348066298342541436464088397790055248618784530386740331491712707182320441)
1⅄(1⅄2Q)n42=[1⅄2Q=(2⅄Qn43c1/2⅄Qn42c1)]=(0.989637304699481864284974093264248704663212435233160621761658031088082901554404145077720207253886010362694300518134715025906735751295336787564766839378238341917098445595854922279792746113/0.94764397905759162303664921465968586387434554973821989528795811518324607329842931937172774869109)
1⅄(1⅄2Q)n43=[1⅄2Q=(2⅄Qn44c1/2⅄Qn43c1)]=(0.979695431/0.989637304699481864284974093264248704663212435233160621761658031088082901554404145077720207253886010362694300518134715025906735751295336787564766839378238341917098445595854922279792746113)
1⅄(1⅄2Q)n44=[1⅄2Q=(2⅄Qn45c1/2⅄Qn44c1)]=(0.989949748743718592964824120603015075025125628140703517587939698492462311557763819095477386934673366834170854271356783919597/0.979695431)
and so on for variables of ∈1⅄(2⅄2Q)n=[1⅄2Q=(2⅄Qn2cn/2⅄Qn1cn)] that vary to degrees of stem cycle count variant 1⅄(2⅄2Q)ncn
Functions applicable to variables of ∈1⅄(1⅄2Q)ncn=[1⅄2Q=(2⅄Qn2cn/2⅄Qn1cn)]
X⅄=(n2xn1) example X⅄(1⅄2Q)n=[X2Q=(2⅄Qn2cnx2⅄Qn1cn)]
+⅄=(nncn+nncn) example +⅄(1⅄2Q)n=[+⅄2Q=(2⅄Qn2cn+2⅄Qn1cn)]
1-⅄=(n2-n1) example 1-⅄(1⅄2Q)n=[2-⅄2Q=(1⅄Qn2cn-2⅄Qn1cn)]
3rd tier of Q and 4th divide of P prime base quotient ratios
Then example 1⅄(1⅄3Q)n1 of (2⅄2Qn2c1/2⅄2Qn1c1)] so
1⅄(1⅄3Q)n1 of (2⅄2Qn2c1/2⅄2Qn1c1)]=(1.190475/1)=1.190475
1⅄(1⅄3Q)n2 of (2⅄2Qn3c1/2⅄2Qn2c1)]=(0.882000/1.190475)=0.74088 or 0.74088074088
1⅄(1⅄3Q)n3 of (2⅄2Qn4c1/2⅄2Qn4c1)]=(1.3431/0.882000)
1⅄(1⅄3Q)n4 of (2⅄2Qn5c1/2⅄2Qn4c1)]=(0.9037442192522405/1.3431)
1⅄(1⅄3Q)n5 of (2⅄2Qn6c1/2⅄2Qn5c1)]=(1.170040485829959630/0.9037442192522405)
1⅄(1⅄3Q)n6 of (2⅄2Qn7c1/2⅄2Qn6c1)]=(0.9232736572890025584679383631713554996444089514066496172914677749360613819973501278772378525855854219948849114091148337595907937620560102301790290561/1.170040485829959630)
1⅄(1⅄3Q)n7 of (2⅄2Qn8c1/2⅄2Qn7c1)]=(0.960072595281306715063616878306896551724137940635199110707803992741431940963702359346642564246727949183303085309056251742286751361162484572542649727767695195825675317604355716888003620163339382940109852993595281306715063616878306896551724137940635199110707803992741431940963702359346642564246727949183303085309056251742286751361162484572542649727767695195825675317604355716888003620163339382940109852993/0.9232736572890025584679383631713554996444089514066496172914677749360613819973501278772378525855854219948849114091148337595907937620560102301790290561)
1⅄(1⅄3Q)n8 of (2⅄2Qn9c1/2⅄2Qn8c1)]=[(2⅄Qn10c1/2⅄Qn9c1)/(2⅄Qn9c1/2⅄Qn8c1)]
1⅄(1⅄3Q)n9 of (2⅄2Qn10c1/2⅄2Qn9c1)]=[(2⅄Qn11c1/2⅄Qn10c1)/(2⅄Qn10c1/2⅄Qn9c1)]
and so on for variables of ∈1⅄(1⅄3Q)ncn of (2⅄2Qn2c1/2⅄2Qn1c1)] from 2⅄Q variables of Prime P base consecutives
4th tier of Q and 5th divide of P prime base quotient ratios
Then example 1⅄(1⅄4Q)n1 of [(1⅄(1⅄3Q)n2~(2⅄2Qn3c1/2⅄2Qn2c1)]/2⅄2Qn1c1) / 1⅄(1⅄3Q)n1~(2⅄2Qn2c1/2⅄2Qn1c1)]] so
1⅄(1⅄4Q)n1 of [(1⅄(1⅄3Q)n2/1⅄(1⅄3Q)n1=[(0.^882000/1.190475)/(1.190475/1)]=(0.74088/1.190475)=0.6^223398
1⅄(1⅄4Q)n2 of [(1⅄(1⅄3Q)n3/1⅄(1⅄3Q)n2=[(2⅄2Qn4c1/2⅄2Qn4c1)/(2⅄2Qn3c1/2⅄2Qn2c1)]
and so on for variables of ∈1⅄(1⅄4Q)n1 of [(1⅄(1⅄3Q)n2/1⅄(1⅄3Q)n1 from variables of ∈1⅄(1⅄3Q)ncn of (2⅄2Qn2c1/2⅄2Qn1c1)] derived from 2⅄Q variables of Prime P base consecutives
Prime ∈1⅄2Q and ∈2⅄2Q Base Path Variants
∈1⅄1Qn1 and ∈2⅄1Qn1 with definition of 3⅄ and 2⅄ and 1⅄ sets in prime base of p division logic.
As 3⅄ is not applicable to prime p numerals having no decimal cn change until decimal ratio cell stem cycles are a Q factor.
2⅄ and 1⅄ are paths of p prime consecutive numerals that divide later and previous as explained.
Now paths of two different Q bases labelled as 1Qn1 are in fact not simply 1Qn1
1⅄1Qn1 and 2⅄1Qn1 are paths of p prime consecutive numerals 2⅄ and 1⅄
Each of the variant paths of ⅄1Q can then be reapplied to their own three variant paths 3⅄ and 2⅄ and 1⅄ forming new sets that are not the same sets where cn is a variant factor in each set of the next tier stems cycles and cell definitions.
Variables of sets explained below are applicable to functions with prime p fibonacci y and phi φn base numerals through paths 1⅄, 2⅄, 1X, 1+⅄, 1-⅄, 2-⅄, 3⅄nc ⅄n ⅄ncn numerically.
∈1⅄2Q and ∈2⅄2Q and ∈3⅄2Q then require further definition or symbol notation.
∈1⅄2
∈1⅄2Qn1 of ∈1⅄1Qn1 variables is (1⅄1Qn2/1⅄1Qn1)=(1.6/1.5)=1.06 for 1⅄1Qn2c1 variable and (1⅄1Qn2c2/1⅄1Qn1)=(1.66/1.5)=1.106 and so on depending of cn variable factor
∈1⅄2Qn1 of ∈2⅄1Qn1 variables is (2⅄1Qn2/2⅄1Qn1)=(0.6/0.6)=1 for 2⅄1Qn1c1 variable and (2⅄1Qn2/2⅄1Qn1c2)=(0.6/0.66)=1.1 and so on depending of cn variable factor
then
∈1⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn2/2⅄1Qn1)=(1.6/0.6)=2.6 depending of cn variable factor c1
and
∈1⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn2/1⅄1Qn1)=(0.6/1.5)=0.4
and are crossed variants of two different path sets variables
∈2⅄2
∈2⅄2Qn1 of ∈1⅄1Qn1 variables is (1⅄1Qn1/1⅄1Qn2)
∈2⅄2Qn1 of ∈2⅄1Qn1 variables is (2⅄1Qn1/2⅄1Qn2)
then
∈2⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn1/2⅄1Qn2) depending of cn variable factor
and
∈2⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn1/1⅄1Qn2) depending of cn variable factor
and are crossed variants of two different path sets variables
∈3⅄2
∈3⅄2Qn1 of ∈1⅄1Qn1 variables is (1⅄1Qn1cn/1⅄1Qn1cn)
∈3⅄2Qn1 of ∈2⅄1Qn1 variables is (2⅄1Qn1cn/2⅄1Qn1cn)
then
∈3⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn1cn/2⅄1Qn1cn) depending of cn variable factor
and
∈3⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn1cn/1⅄1Qn2cn) depending of cn variable factor
and are crossed variants of two different path sets variables
Sets are factorable with AND differ from THESE VARIABLES DEFINITIONS
3rd tiers of Q alternate paths from prime base of ∈3⅄1Qcn sets
∈3⅄(1⅄1Qn)cn/(2⅄1Qn)cn are not same set ∉ yet path of 3⅄ defines variables of same tier level and cn differential factors
and
∈3⅄(2⅄1Qn)cn/(1⅄1Qn)cn are not same set ∉ yet path of 3⅄ defines variables of same tier level and cn differential factors
and
∈3⅄(1⅄1Qn)cn/(1⅄1Qn)cn
and
∈3⅄(2⅄1Qn)cn/(2⅄1Qn)cn
are applicable ratios to phi and y bases and tiers of the paths of φ of many functions as well as prime path variables sets tiers per variant cycle cn.
∈1⅄ and ∈2⅄ and ∈3⅄ of sets in Q's from P to Y and φ factoring at degrees of cn
∈1⅄3Q=(⅄2Q/⅄2Q)=(⅄1Q/⅄1Q)/(⅄1Q/⅄1Q)=(⅄p/⅄p) that ⅄1Q lacks path root definition of 1⅄1Q or 2⅄1Q from base prime path ⅄P
∈2⅄3Q=(⅄2Q/⅄2Q)=(⅄1Q/⅄1Q)/(⅄1Q/⅄1Q)=(⅄p/⅄p) that ⅄1Q lacks path root definition of 1⅄1Q or 2⅄1Q from base prime path ⅄P
∈3⅄3Q=(⅄2Q/⅄2Q)=(⅄1Q/⅄1Q)/(⅄1Q/⅄1Q)=(⅄p/⅄p) that ⅄1Q lacks path root definition of 1⅄1Q or 2⅄1Q from base prime path ⅄P
So variables of sets ∈1⅄3Q, ∈2⅄3Q, ∈3⅄3Q, ∈1⅄2Q, ∈2⅄2Q, ∈3⅄2Q require definitions of variable from set ∈1⅄1Q or ∈2⅄1Q from base prime path ⅄P.
∈3⅄2Qn1 of ∈1⅄1Qn1 variables is (1⅄1Qn1/1⅄1Qn1)=(1.5/1.5)=1
∈3⅄2Qn2 of ∈1⅄1Qn1 variables is (1⅄1Qn2c1/1⅄1Qn2c2)=(1.6/1.66) and so on for cn differentials. . .
∈3⅄2Qn2 of ∈1⅄1Qn1 variables is (1⅄1Qn2c2/1⅄1Qn2c1)=(1.66/1.6) and so on for cn differentials. . .
∈3⅄2Qn3 of ∈1⅄1Qn1 variables is (1⅄1Qn3/1⅄1Qn3)=(1.4/1.4)=1
∈3⅄2Qn4 of ∈1⅄1Qn1 variables is (1⅄1Qn4c1/1⅄1Qn4c2)=(1.571428/1.571428571428) and so on for cn differentials. . .
∈3⅄2Qn4 of ∈1⅄1Qn1 variables is (1⅄1Qn4c2/1⅄1Qn4c1)=(1.571428571428/1.571428) and so on for cn differentials. . .
∈3⅄2Qn5 of ∈1⅄1Qn1 variables is (1⅄1Qn5c1/1⅄1Qn5c2)=(1.18/1.1818) and so on for cn differentials. . .
∈3⅄2Qn5 of ∈1⅄1Qn1 variables is (1⅄1Qn5c2/1⅄1Qn5c1)=(1.1818/1.18) and so on for cn differentials. . .
∈3⅄2Qn6 of ∈1⅄1Qn1 variables is (1⅄1Qn6c1/1⅄1Qn6c2)=(1.307692/1.307692307692) and so on for cn differentials. . .
∈3⅄2Qn6 of ∈1⅄1Qn1 variables is (1⅄1Qn6c2/1⅄1Qn6c1)=(1.307692307692/1.307692) and so on for cn differentials. . .
∈3⅄2Qn7 of ∈1⅄1Qn1 variables is (1⅄1Qn7c1/1⅄1Qn7c2)=(1.1176470588235294/1.11764705882352941176470588235294) and so on for cn differentials. . .
∈3⅄2Qn7 of ∈1⅄1Qn1 variables is (1⅄1Qn7c2/1⅄1Qn7c1)=(1.11764705882352941176470588235294/1.1176470588235294) and so on for cn differentials. . .
∈3⅄2Qn8 of ∈1⅄1Qn1 variables is (1⅄1Qn8c1/1⅄1Qn8c2)=(1.210526315789473684/1.210526315789473684210526315789473684) and so on for cn differentials. . .
∈3⅄2Qn8 of ∈1⅄1Qn1 variables is (1⅄1Qn8c2/1⅄1Qn8c1)=(1.210526315789473684210526315789473684/1.210526315789473684) and so on for cn differentials. . .
Beginning with
∈3⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn1cn/2⅄1Qn1cn) depending of cn variable factor
∈3⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is
(1⅄1Qn1c1/2⅄1Qn1c1)=(1.5/0.6)
(1⅄1Qn1c1/2⅄1Qn1c2)=(1.5/0.66)
(1⅄1Qn1c1/2⅄1Qn1c3)=(1.5/0.666) and so on for cn variable factor
∈3⅄2Qn2 of ∈1⅄1Qn and ∈2⅄1Qn variables is
(1⅄1Qn2c1/2⅄1Qn2c1)=(1.6/0.6)
(1⅄1Qn2c2/2⅄1Qn2c1)=(1.66/0.6)
(1⅄1Qn2c3/2⅄1Qn2c1)=(1.666/0.6) and so on for cn variable factor
∈3⅄2Qn3 of ∈1⅄1Qn and ∈2⅄1Qn variables is
(1⅄1Qn3c1/2⅄1Qn3c1)=(1.4/0.714285)
(1⅄1Qn3c1/2⅄1Qn3c2)=(1.4/0.714285714285)
(1⅄1Qn3c1/2⅄1Qn3c3)=(1.4/0.714285714285714285) and so on for cn variable factor
∈3⅄2Qn4 of ∈1⅄1Qn and ∈2⅄1Qn variables is
(1⅄1Qn4c1/2⅄1Qn4c1)=(1.571428/0.63)
(1⅄1Qn4c1/2⅄1Qn4c2)=(1.571428/0.6363)
(1⅄1Qn4c2/2⅄1Qn4c1)=(1.571428571428/0.63)
(1⅄1Qn4c3/2⅄1Qn4c2)=(1.571428571428571428/0.6363)
(1⅄1Qn4c2/2⅄1Qn4c3)=(1.571428571428/0.636363)
(1⅄1Qn4c3/2⅄1Qn4c1)=(1.571428571428571428/0.63)
(1⅄1Qn4c1/2⅄1Qn4c3)=(1.571428/0.636363) and so on for cn variable factor
∈3⅄2Qn5 of ∈1⅄1Qn and ∈2⅄1Qn variables is
(1⅄1Qn5c1/2⅄1Qn5c1)=(1.18/0.846153)
(1⅄1Qn5c1/2⅄1Qn5c2)=(1.18/0.846153846153)
(1⅄1Qn5c2/2⅄1Qn5c1)=(1.1818/0.846153) and so on for cn variable factor
∈3⅄2Qn6 of ∈1⅄1Qn and ∈2⅄1Qn variables is
(1⅄1Qn6c1/2⅄1Qn6c1)=(1.307692/0.7647058823529411)
(1⅄1Qn6c1/2⅄1Qn6c2)=(1.307692/0.76470588235294117647058823529411)
(1⅄1Qn6c2/2⅄1Qn6c1)=(1.307692307692/0.7647058823529411) and so on for cn variable factor
∈3⅄2Qn7 of ∈1⅄1Qn and ∈2⅄1Qn variables is
(1⅄1Qn7c1/2⅄1Qn7c1)=(1.1176470588235294/0.894736842105263157)
(1⅄1Qn7c1/2⅄1Qn7c2)=(1.1176470588235294/0.894736842105263157894736842105263157)
(1⅄1Qn7c2/2⅄1Qn7c1)=(1.11764705882352941176470588235294/0.894736842105263157) and so on for cn variable factor
∈3⅄2Qn8 of ∈1⅄1Qn and ∈2⅄1Qn variables is
(1⅄1Qn8c1/2⅄1Qn8c1)=(1.210526315789473684/0.8260869565217391304347)
(1⅄1Qn8c1/2⅄1Qn8c2)=(1.210526315789473684/0.82608695652173913043478260869565217391304347)
(1⅄1Qn8c2/2⅄1Qn8c1)=(1.210526315789473684210526315789473684/0.8260869565217391304347) and so on for cn variable factor
Beginning with
∈3⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn1cn/1⅄1Qn2cn) depending of cn variable factor
∈3⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is
(2⅄1Qn1c1/1⅄1Qn1c1)=(0.6/1.5)
(2⅄1Qn1c2/1⅄1Qn1c1)=(0.66/1.5)
(2⅄1Qn1c3/1⅄1Qn1c1)=(0.666/1.5) and so on for cn variable factor
∈3⅄2Qn2 of ∈2⅄1Qn and ∈1⅄1Qn variables is
(2⅄1Qn2c1/1⅄1Qn2c1)=(0.6/1.6)
(2⅄1Qn2c1/1⅄1Qn2c2)=(0.6/1.66)
(2⅄1Qn2c1/1⅄1Qn2c3)=(0.6/1.666) and so on for cn variable factor
∈3⅄2Qn3 of ∈2⅄1Qn and ∈1⅄1Qn variables is
(2⅄1Qn3c1/1⅄1Qn3c1)=(0.714285/1.4)
(2⅄1Qn3c2/1⅄1Qn3c1)=(0.714285714285/1.4)
(2⅄1Qn3c3/1⅄1Qn3c1)=(0.714285714285714285/1.4) and so on for cn variable factor
∈3⅄2Qn4 of ∈2⅄1Qn and ∈1⅄1Qn variables is
(2⅄1Qn4c1/1⅄1Qn4c1)=(0.63/1.571428)
(2⅄1Qn4c1/1⅄1Qn4c2)=(0.63/1.571428571428)
(2⅄1Qn4c2/1⅄1Qn4c1)=(0.6363/1.571428)
(2⅄1Qn4c3/1⅄1Qn4c2)=(0.636363/1.571428571428)
(2⅄1Qn4c2/1⅄1Qn4c3)=(0.6363/1.571428571428571428)
(2⅄1Qn4c3/1⅄1Qn4c1)=(0.636363/1.571428)
(2⅄1Qn4c1/1⅄1Qn4c3)=(0.63/1.571428571428571428) and so on for cn variable factor
∈3⅄2Qn5 of ∈2⅄1Qn and ∈1⅄1Qn variables is
(2⅄1Qn5c1/1⅄1Qn5c1)=(0.846153/1.18)
(2⅄1Qn5c1/1⅄1Qn5c2)=(0.846153/1.1818)
(2⅄1Qn5c2/1⅄1Qn5c1)=(0.846153846153/1.18) and so on for cn variable factor
∈3⅄2Qn6 of ∈2⅄1Qn and ∈1⅄1Qn variables is
(2⅄1Qn6c1/1⅄1Qn6c1)=(0.7647058823529411/1.307692)
(2⅄1Qn6c1/1⅄1Qn6c2)=(0.7647058823529411/1.307692307692)
(2⅄1Qn6c2/1⅄1Qn6c1)=(0.76470588235294117647058823529411/1.307692) and so on for cn variable factor
∈3⅄2Qn7 of ∈2⅄1Qn and ∈1⅄1Qn variables is
(2⅄1Qn7c1/1⅄1Qn7c1)=(0.894736842105263157/1.1176470588235294)
(2⅄1Qn7c1/1⅄1Qn7c2)=(0.894736842105263157/1.11764705882352941176470588235294)
(2⅄1Qn7c2/1⅄1Qn7c1)=(0.894736842105263157894736842105263157/1.1176470588235294) and so on for cn variable factor
∈3⅄2Qn8 of ∈2⅄1Qn and ∈1⅄1Qn variables is
(2⅄1Qn8c1/1⅄1Qn8c1)=(0.8260869565217391304347/1.210526315789473684)
(2⅄1Qn8c1/1⅄1Qn8c2)=(0.8260869565217391304347/1.210526315789473684210526315789473684)
(2⅄1Qn8c2/1⅄1Qn8c1)=(0.82608695652173913043478260869565217391304347/1.210526315789473684) and so on for cn variable factor
Tier base ratio sets and paths of the variables of 1φn1/pn1 and pn1/φn1
∈3⅄(1φn1/pn1)/(pn1/φn1)=(0/0)=0 and form more complex scale sets and tier variables of set
∈3⅄(pn1/φn1)/(1φn1/pn1)=(0/0)=0 and form more complex scale sets and tier variables of set
∈2⅄(1φn1/pn1)/(pn2/φn2) =(0/3)=0 and form more complex scale sets and tier variables of set
∈2⅄(pn1/φn1)/(1φn2/pn2) =(0/0.^3)=0 and form more complex scale sets and tier variables of set
∈1⅄(1φn2/pn2)/(pn1/φn1)=(0.^3/0)=0 and form more complex scale sets and tier variables of set
∈1⅄(pn2/φn2)/(1φn1/pn1)=(3/0)=0 and form more complex scale sets and tier variables of set
Variable stem paths determined in factoring for (φn/pn)cn and (pn/φn)cn of sets ∈1⅄, 2⅄, 1X, 1+⅄, 1-⅄, 2-⅄, 3⅄nc ⅄n ⅄ncn
Because of the complexity and decimal length of the variable factors with potential change given cn a short scale of examples will be displayed below and as the previous numerals have shown, extreme precision can be factored of these arc variable definitions.
Alternate combinations of sequences and variables can be factored that are real numbers defined.
For now here are the basics of this fractal polarization in quantum field variables assuming cn is one cycle stem to two
BASE SET of ∈3⅄φn/pn
∈3⅄(1φn1/pn1)/(pn1/φn1)=(0/0)=0
∈3⅄(1φn2/pn2)/(pn2/φn2)=(0.3/3)=0.1 and ∈3⅄(1φn2/pn2)c2/(pn2/φn2)=(0.33/3)=0.11 and so on . . .
∈3⅄(1φn3/pn3)/(pn1/φn3)=(0.4/2.5)=0.16
∈3⅄(1φn4/pn4)/(pn4/φn4)=(0.2142857/4)=0.053571425
and ∈3⅄(1φn4/pn4)c2/(pn4/φn4)=(0.2142857/4)=0.053571428571425
∈3⅄(1φn5/pn5)/(pn5/φn5)=(1.45/6.875)
and ∈3⅄(1φn5c2/pn5)/(pn5/φn5c2)=(0.1509/6.626506024096084337349397590361445784337951712047)
and ∈3⅄(1φn5/pn5)/(pn5/φn5c2)=(1.45/6.626506024096084337349397590361445784337951712047)
and ∈3⅄(1φn5c2/pn5)/(pn5/φn5c2)=(0.1509/6.875) of ∈3⅄(1φn5/pn5)/(pn5/φn5)c1 bases
alternate paths variable function examples ∈3⅄(1φn5/pn5)c2/(pn5/φn5)=(1.4545/6.875)
and ∈3⅄(1φn5c2/pn5)c2/(pn5/φn5c2)=(0.15099/6.626506024096084337349397590361445784337951712047)
and ∈3⅄(1φn5c2/pn5)c2/(pn5/φn5c2)c2=(0.15099/6.62650602409608433734939759036144578433795171204724096084337349397590361445784337951712047)
and ∈3⅄(1φn5c2/pn5)/(pn5/φn5c2)c2=(0.1509/6.62650602409608433734939759036144578433795171204724096084337349397590361445784337951712047)
and ∈3⅄(1φn5/pn5)c2/(pn5/φn5c2)=(1.4545/6.626506024096084337349397590361445784337951712047)
and ∈3⅄(1φn5/pn5)c2/(pn5/φn5c2)c2=(1.4545/6.62650602409608433734939759036144578433795171204724096084337349397590361445784337951712047)
and ∈3⅄(1φn5/pn5)/(pn5/φn5c2)c2=(1.45/6.62650602409608433734939759036144578433795171204724096084337349397590361445784337951712047)
and ∈3⅄(1φn5c2/pn5)c2/(pn5/φn5c2)=(0.15099/6.875) and ∈3⅄(1φn5c2/pn5)c3/(pn5/φn5c2)=(0.150999/6.875) variants
∈3⅄(1φn6/pn6)/(pn6/φn6)=(0.1230769/8.125) and ∈3⅄(1φn6/pn6)c2/(pn6/φn6)=(0.1230769230769/8.125)
∈3⅄(1φn7/pn7)/(pn7/φn7)=(0.0955882352941176470/10.4615076923)
∈3⅄(1φn7/pn7)c2/(pn7/φn7)=(0.09558823529411764705882352941176470/10.4615076923)
∈3⅄(1φn7/pn7)c2/(pn7/φn7)c2=(0.09558823529411764705882352941176470/10.461507692376923)
∈3⅄(1φn7/pn7)/(pn7/φn7)c2=(0.0955882352941176470/10.4615076923)
and so on . . . for BASE SET of ∈3⅄φn/pn applicable to a basis of (∈3⅄φn/pn)ncn variable stem cycles cells
BASE SET of ∈3⅄pn/φn
∈3⅄(pn1/φn1)/(1φn1/pn1)=(0/0)=0
∈3⅄(pn2/φn2)/(1φn2/pn2)=(3/0.3)
∈3⅄(pn3/φn3)/(1φn3/pn3)=(2.5/0.4)
∈3⅄(pn4/φn4)/(1φn4/pn4)=(4/0.2142857)
∈3⅄(pn5/φn5)/(1φn5/pn5)=(6.875/1.45)
and ∈3⅄(pn5/φn5c2)/(1φn5c2/pn5)=(6.626506024096084337349397590361445784337951712047/0.1509)
and ∈3⅄(pn5/φn5c2)/(1φn5/pn5)=(6.626506024096084337349397590361445784337951712047)/1.45)
and ∈3⅄(pn5/φn5)/(1φn5c2/pn5)=(6.875/0.1509) of ∈3⅄(pn5/φn5)/(1φn5/pn5) bases in c1 and c2
∈3⅄(pn6/φn6)/(1φn6/pn6)=(8.125/0.1230769)
∈3⅄(pn7/φn7)/(1φn7/pn7)=(10.4615076923/0.0955882352941176470)
and so on . . . for BASE SET of ∈3⅄pn/φn applicable to a basis of (∈3⅄pn/φn)ncn variable stem cycles cells
BASE SET of ∈2⅄φn/pn
∈2⅄(1φn1/pn1)/(pn2/φn2) =(0/3)=0
∈2⅄(1φn2/pn2)/(pn3/φn3) =(0.3/2.5)
∈2⅄(1φn3/pn3)/(pn4/φn4) =(0.4/4)
∈2⅄(1φn4/pn4)/(pn5/φn5) =(0.2142857/6.875)
and ∈2⅄(1φn4/pn4)/(pn5/φn5c2) =(0.2142857/6.626506024096084337349397590361445784337951712047)
of ∈2⅄(1φn4/pn4)/(pn5/φn5) bases to ∈2⅄(1φn4/pn4)/(pn5/φn5c2)
∈2⅄(1φn5/pn5)/(pn6/φn6) =(1.45/8.125)
and ∈2⅄(1φn5c2/pn5)/(pn6/φn6) =(0.1509/8.125) of ∈2⅄(1φn5/pn5)/(pn6/φn6) to ∈2⅄(1φn5c2/pn5)/(pn6/φn6) bases
∈2⅄(1φn6/pn6)/(pn7/φn7) =(0.1230769/10.4615076923)
and so on . . . for BASE SET of ∈2⅄φn/pn applicable to a basis of (∈2⅄φn/pn)ncn variable stem cycles cells
BASE SET of ∈2⅄pn/φn
∈2⅄(pn1/φn1)/(1φn2/pn2) =(0/0.3)=0
∈2⅄(pn2/φn2)/(1φn3/pn3) =(3/0.4)
∈2⅄(pn3/φn3)/(1φn4/pn4) =(2.5/0.2142857)
∈2⅄(pn4/φn4)/(1φn5/pn5) =(4/1.45)
and ∈2⅄(pn4/φn4)/(1φn5c2/pn5) =(4/0.1509) of ∈2⅄(pn4/φn4)/(1φn5/pn5) to ∈2⅄(pn4/φn4)/(1φn5c2/pn5) bases
∈2⅄(pn5/φn5)/(1φn6/pn6) =(6.875/0.1230769)
and ∈2⅄(pn5/φn5c2)/(1φn6/pn6) =(6.626506024096084337349397590361445784337951712047/0.1230769)
of ∈2⅄(pn5/φn5)/(1φn6/pn6) to ∈2⅄(pn5/φn5c2)/(1φn6/pn6) bases
∈2⅄(pn6/φn6)/(1φn7/pn7) =(8.125/0.0955882352941176470)
∈2⅄(pn7/φn7)/(1φn8/pn8) =(10.4615076923/0.079757052631578421)
and ∈2⅄(pn7/φn7)/(1φn8c2/pn8) =(10.4615076923/0.079757079757052631578421)
of ∈2⅄(pn7/φn7)/(1φn8/pn8) to ∈2⅄(pn7/φn7)/(1φn8c2/pn8) bases
and so on . . . for BASE SET of ∈2⅄pn/φn applicable to a basis of (∈2⅄pn/φn)ncn variable stem cycles cells
BASE SET of 1⅄φn/pn
∈1⅄(1φn2/pn2)/(pn1/φn1)=(0.3/0)=0
∈1⅄(1φn3/pn3)/(pn2/φn2)=(0.4/3)
∈1⅄(1φn4/pn4)/(pn3/φn3)=(0.2142857/2.5)
∈1⅄(1φn5/pn5)/(pn4/φn4)=(1.45/4)
∈1⅄(1φn6/pn6)/(pn5/φn5)=(0.1230769/6.875)
and ∈1⅄(1φn6/pn6)/(pn5/φn5c2)=(0.1230769/6.626506024096084337349397590361445784337951712047)
of ∈1⅄(1φn6/pn6)/(pn5/φn5) to ∈1⅄(1φn6/pn6)/(pn5/φn5c2) bases
∈1⅄(1φn7/pn7)/(pn6/φn6)=(0.0955882352941176470/8.125)
∈1⅄(1φn8/pn8)/(pn7/φn7)=(0.079757052631578421/10.4615076923)
and ∈1⅄(1φn8c2/pn8)/(pn7/φn7)=(0.079757079757052631578421/10.4615076923)
of ∈1⅄(1φn8/pn8)/(pn7/φn7) to ∈1⅄(1φn8c2/pn8)/(pn7/φn7) bases
and so on . . . for BASE SET of 1⅄φn/pn applicable to a basis of (1⅄φn/pn)ncn variable stem cycles cells
BASE SET of ∈1⅄pn/φn
∈1⅄(pn2/φn2)/(1φn1/pn1)=(3/0)=0
∈1⅄(pn3/φn3)/(1φn2/pn2)=(2.5/0.3)
∈1⅄(pn4/φn4)/(1φn3/pn3)=(4/0.4)
∈1⅄(pn5/φn5)/(1φn4/pn4)=(6.875/0.2142857)
and ∈1⅄(pn5/φn5c2)/(1φn4/pn4)=(6.626506024096084337349397590361445784337951712047/0.2142857)
of ∈1⅄(pn5/φn5)/(1φn4/pn4) to ∈1⅄(pn5/φn5c2)/(1φn4/pn4) bases
∈1⅄(pn6/φn6)/(1φn5/pn5)=(8.125/1.45)
and ∈1⅄(pn6/φn6)/(1φn5c2/pn5)=(8.125/0.1509)
of ∈1⅄(pn6/φn6)/(1φn5/pn5) to ∈1⅄(pn6/φn6)/(1φn5c2/pn5) bases
∈1⅄(pn7/φn7)/(1φn6/pn6)=(10.4615076923/0.1230769)
and so on . . . for BASE SET of ∈1⅄pn/φn applicable to a basis of (∈1⅄pn/φn)ncn variable stem cycles cells
Similar term base numerals and path difference mid phase variables later related in equations
For simplicity a few base variables will be used here to explain paths of similar terms and variables expressed from the similar terms that become quadratic equations with decimal number variables in further terms from the same numeral sequences explained. a simple error can cause extreme inaccuracy with this simple logic factored incorrectly.
From Y and P limit to ten digits 2 : 3 : 5 : 13 : 89 : 1597 : 28657 : 514229 : 433494437 are common factors.
Phi Theta Θ φ Q scale set paths and functions of cn stem cycle cell groups from y and p bases
123⅄ncn|Θ/Y|ncn 123⅄ncn|Y/Θ|ncn 123⅄ncn|YxΘ|ncn 123⅄ncn|Y+Θ|ncn 123⅄ncn|Y-Θ|ncn 123⅄ncn|Θ-Y|ncn
123⅄ncn|Θ/φ|ncn 123⅄ncn|φ/Θ|ncn 123⅄ncn|φxΘ|ncn 123⅄ncn|φ+Θ|ncn 123⅄ncn|φ-Θ|ncn 123⅄ncn|φ-Θ|ncn
123⅄ncn|Θ/P|ncn 123⅄ncn|P/Θ|ncn 123⅄ncn|PxΘ|ncn 123⅄ncn|P+Θ|ncn 123⅄ncn|P-Θ|ncn 123⅄ncn|Θ-P|ncn
123⅄ncn|Θ/Q|ncn 123⅄ncn|Q/Θ|ncn 123⅄ncn|QxΘ|ncn 123⅄ncn|Q+Θ|ncn 123⅄ncn|Q-Θ|ncn 123⅄ncn|Θ-Q|ncn
Phi Prime Theta Ratio sets of y p base variables
123⅄ncn|A/Θn|ncn 123⅄ncn|Θn/A|ncn
123⅄ncn|M/Θn|ncn 123⅄ncn|Θn/M|ncn
123⅄ncn|V/Θn|ncn 123⅄ncn|Θn/V|ncn
123⅄ncn|W/Θn|ncn 123⅄ncn|Θn/W|ncn
123⅄ncn|ᐱ/Θn|ncn 123⅄ncn|Θn/ᐱ|ncn
123⅄ncn|ᗑ/Θn|ncn 123⅄ncn|Θn/ᗑ|ncn
AM and VW paths in wave functions of cycle variants 1⅄, 2⅄, 3⅄
A=∈1⅄(φ/Q)cn and path ⅄ of Q is a variant in the definition of A
M=∈2⅄(φ/Q)cn and path ⅄ of Q is a variant in the definition of M
V= ∈1⅄(Q/φ)cn and path ⅄ of Q is a variant in the definition of V
W=∈2⅄(Q/φ)cn and path ⅄ of Q is a variant in the definition of W
that 3⅄A, 3⅄M, 3⅄V, 3⅄W vary from
3⅄A of A=∈1⅄(φ/Q)cn and path ⅄ of Q is a variant in the definition of A
3⅄M of M=∈2⅄(φ/Q)cn and path ⅄ of Q is a variant in the definition of M
3⅄V of V= ∈1⅄(Q/φ)cn and path ⅄ of Q is a variant in the definition of V
3⅄W of W=∈2⅄(Q/φ)cn and path ⅄ of Q is a variant in the definition of W
Given A=∈1⅄(φ/Q)cn
The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.
so
A=∈1⅄(φn2/1⅄Qn1)cn
and
A=∈1⅄(φn2/2⅄Qn1)cn
then
An1 of 1⅄(φn2/1⅄Qn1)=(1/1.5)=0.6
An2 of 1⅄(φn3/1⅄Qn2)=(2/1.6)=1.25 and An2 of 1⅄(φn3/1⅄Qn2c2)=(2/1.66)=1.2048192771084337349397590361445783132530
An3 of 1⅄(φn4/1⅄Qn3)=(1.5/1.4)=1.0714285
An4 of 1⅄(φn5/1⅄Qn4)=(1.6/1.571428) and An4 of 1⅄(φn5c2/1⅄Qn4)=(1.66/1.571428) and An4 of 1⅄(φn5/1⅄Qn4)=(1.6/1.571428571428) and An4 of 1⅄(φn5/1⅄Qn4)=(1.66/1.571428571428) and so on for cn variant of An4 of 1⅄(φn5/1⅄Qn4)
An5 of 1⅄(φn6/1⅄Qn5)=(1.6/1.18)=0.988875154511742892459826946847960444993819530284301606922126081582200247218788627935723114956736711990111248454882571075401730531520395550061804697156983930778739184177997527812113720642768850432632880
An6 of 1⅄(φn7/1⅄Qn6)=(1.625/1.307692)
An7 of 1⅄(φn8/1⅄Qn7)=(1.615384/1.1176470588235294)
An8 of 1⅄(φn9/1⅄Qn8)=(1.619047/1.210526315789473684)
An9 of 1⅄(φn10/1⅄Qn9)=(1.61762941/1.268695652173913043478)
An10 of 1⅄(φn11/1⅄Qn10)=(1.618/1.0689655172413793103448275862)
An11 of 1⅄(φn12/1⅄Qn11)=(1.61797752808988764044943820224719101123595505/1.193548387096774)
An12 of 1⅄(φn13/1⅄Qn12)=(1.61805/1.108)
An13 of 1⅄(φn14/1⅄Qn13)=(1.61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832/1.04878)
An14 of 1⅄(φn15/1⅄Qn14)=(1.61830223896551724135014/1.093023255813953488372)
An15 of 1⅄(φn16/1⅄Qn15)=(1.618032786885245901639344262295081967213114754098360655737704918/1.12765957446808510638297872340425531914893610702)
An16 of 1⅄(φn17/1⅄Qn16)=(1.6180344478216818642350572441742654508601925025329280648429584599797365754812563323201418439716312056737588652482269503546099290780141843/1.1132075471698)
An17 of 1⅄(φn18/1⅄Qn17)=(1.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/1.0338983050847457627118644067796610169491525423728813559322)
An18 of 1⅄(φn19/1⅄Qn18)=(1.618034055731424148606811145510835913312693/1.098360655737704918032786885245901639344262295081967213114754)
An19 of 1⅄(φn20/1⅄Qn19)=(1.61803396316670629036115761779478593637885673283903372398947620186558239655584788327911265247548433389141353743123654628079406840468787371442238722793590050227218368811289165271466156421908634298014828988280315713944032525711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242/1.059701492537313432835820895522388)
An20 of 1⅄(φn21/1⅄Qn20)=(1.61803399852/1.02816901408450704225352112676056338)
An21 of 1⅄(φn22/1⅄Qn21)=(1.6180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981/1.08219178)
An22 of 1⅄(φn23/1⅄Qn22)=(1.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793292304217717802495624188357517983174298458585060132121280560103890237705381401388967308452374230704082208796792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869/1.0506329113924) and so on for variables of cn to set variables beyond An22 of 1⅄(φn23/1⅄Qn22) of ∈An of ⅄(φn2/1⅄Qn1)cn
so if A=∈1⅄(φn2/1⅄Qn1)cn
and
A=∈1⅄(φn2/2⅄Qn1)cn
then
An1 of 1⅄(φn2/2⅄Qn1)=(1/0.6)
An2 of 1⅄(φn3/2⅄Qn2)=(2/0.6)
An3 of 1⅄(φn4/2⅄Qn3)=(1.5/0.714285)
An4 of 1⅄(φn5/2⅄Qn4)=(1.6/0.63)
An5 of 1⅄(φn6/2⅄Qn5)=(1.6/0.846153)
An6 of 1⅄(φn7/2⅄Qn6)=(1.625/0.7647058823529411)
An7 of 1⅄(φn8/2⅄Qn7)=(1.615384/0.894736842105263157)
An8 of 1⅄(φn9/2⅄Qn8)=(1.619047/0.8260869565217391304347)
Functions then X, +⅄, and -⅄ of set A variables φn/1⅄Qn and φn/2⅄Qn replaced where functions of division paths 1⅄, 2⅄, and 3⅄ formulate A of X(φnx1⅄Qn), A of X(φnx2⅄Qn), A of +⅄(φnx+1⅄Qn), A of +⅄(φn+2⅄Qn), A of -⅄(φn-1⅄Qn), and A of -⅄(φn-2⅄Qn) so then
if A of X(φnx1⅄Qn) and A of X(φnx2⅄Qn) then
An1 of X(φn2x1⅄Qn1)=(1x1.5)
An2 of X(φn3x1⅄Qn2)=(2x1.6)
An3 of X(φn4x1⅄Qn3)=(1.5x1.4)
An4 of X(φn5x1⅄Qn4)=(1.6x1.571428)
An5 of X(φn6x1⅄Qn5)=(1.6x1.18)
An6 of X(φn7x1⅄Qn6)=(1.625x1.307692)
An7 of X(φn8x1⅄Qn7)=(1.615384x1.1176470588235294)
An8 of X(φn9x1⅄Qn8)=(1.619047x1.210526315789473684)
so if A of X(φn2x1⅄Qn1)cn
and
A of X(φn2x2⅄Qn1)cn
then
An1 of X(φn2x2⅄Qn1)=(1x0.6)
An2 of X(φn3x2⅄Qn2)=(2x0.6)
An3 of X(φn4x2⅄Qn3)=(1.5x0.714285)
An4 of X(φn5x2⅄Qn4)=(1.6x0.63)
An5 of X(φn6x2⅄Qn5)=(1.6x0.846153)
An6 of X(φn7x2⅄Qn6)=(1.625x0.7647058823529411)
An7 of X(φn8x2⅄Qn7)=(1.615384x0.894736842105263157)
An8 of X(φn9x2⅄Qn8)=(1.619047x0.8260869565217391304347)
AND IF A of +⅄(φnx+1⅄Qn) then A of +⅄(φn+2⅄Qn)then
An1 of +⅄(φn2+1⅄Qn1)=(1+1.5)
An2 of +⅄(φn3+1⅄Qn2)=(2+1.6)
An3 of +⅄(φn4+1⅄Qn3)=(1.5+1.4)
An4 of +⅄(φn5+1⅄Qn4)=(1.6+1.571428)
An5 of +⅄(φn6+1⅄Qn5)=(1.6+1.18)
An6 of +⅄(φn7+1⅄Qn6)=(1.625+1.307692)
An7 of +⅄(φn8+1⅄Qn7)=(1.615384+1.1176470588235294)
An8 of +⅄(φn9+1⅄Qn8)=(1.619047+1.210526315789473684)
so if A of +⅄(φn2+1⅄Qn1)cn
and
A of +⅄(φn2+2⅄Qn1)cn
then
An1 of +⅄(φn2+2⅄Qn1)=(1+0.6)
An2 of +⅄(φn3+2⅄Qn2)=(2+0.6)
An3 of +⅄(φn4+2⅄Qn3)=(1.5+0.714285)
An4 of +⅄(φn5+2⅄Qn4)=(1.^6+0.63)
An5 of +⅄(φn6+2⅄Qn5)=(1.6+0.846153)
An6 of +⅄(φn7+2⅄Qn6)=(1.625+0.7647058823529411)
An7 of +⅄(φn8+2⅄Qn7)=(1.615384+0.894736842105263157)
An8 of +⅄(φn9+2⅄Qn8)=(1.619047+0.8260869565217391304347)
AND IF A of -⅄(φnx-1⅄Qn) then A of -⅄(φn-2⅄Qn)then
An1 of -⅄(φn2-1⅄Qn1)=(1-1.5)
An2 of -⅄(φn3-1⅄Qn2)=(2-1.6)
An3 of -⅄(φn4-1⅄Qn3)=(1.5-1.4)
An4 of -⅄(φn5-1⅄Qn4)=(1.6-1.571428)
An5 of -⅄(φn6-1⅄Qn5)=(1.6-1.18)
An6 of -⅄(φn7-1⅄Qn6)=(1.625-1.307692)
An7 of -⅄(φn8-1⅄Qn7)=(1.615384-1.1176470588235294)
An8 of -⅄(φn9-1⅄Qn8)=(1.619047-1.210526315789473684)
so if A of -⅄(φn2-1⅄Qn1)cn
and
A of -⅄(φn2-2⅄Qn1)cn
then
An1 of -⅄(φn2-2⅄Qn1)=(1-0.6)
An2 of -⅄(φn3-2⅄Qn2)=(2-0.6)
An3 of -⅄(φn4-2⅄Qn3)=(1.5-0.714285)
An4 of -⅄(φn5-2⅄Qn4)=(1.6-0.63)
An5 of -⅄(φn6-2⅄Qn5)=(1.6-0.846153)
An6 of -⅄(φn7-2⅄Qn6)=(1.625-0.7647058823529411)
An7 of -⅄(φn8-2⅄Qn7)=(1.615384-0.894736842105263157)
An8 of -⅄(φn9-2⅄Qn8)=(1.619047-0.8260869565217391304347)
THEN IF M=∈2⅄(φ/Q)cn
The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.
so
M=∈2⅄(φn1/1⅄Qn2)cn
and
M=∈2⅄(φn1/2⅄Qn2)cn
then
Mn1 of ∈2⅄(φn1/1⅄Qn2)=(0/1.6)
Mn2 of ∈2⅄(φn2/1⅄Qn3)=(1/1.4)
Mn3 of ∈2⅄(φn3/1⅄Qn4)=(2/1.571428)
Mn4 of ∈2⅄(φn4/1⅄Qn5)=(1.5/1.18)
Mn5 of ∈2⅄(φn5/1⅄Qn6)=(1.6/1.307692)
Mn6 of ∈2⅄(φn6/1⅄Qn7)=(1.6/1.1176470588235294)
Mn7 of ∈2⅄(φn7/1⅄Qn8)=(1.625/1.210526315789473684)
if M=∈2⅄(φn1/1⅄Qn2)cn
and
M=∈2⅄(φn1/2⅄Qn2)cn
then
Mn1 of ∈2⅄(φn1/2⅄Qn2)=(0/0.6)
Mn2 of ∈2⅄(φn2/2⅄Qn3)=(1/0.714285)
Mn3 of ∈2⅄(φn3/2⅄Qn4)=(2/0.63)
Mn4 of ∈2⅄(φn4/2⅄Qn5)=(1.5/0.846153)
Mn5 of ∈2⅄(φn5/2⅄Qn6)=(1.6/0.7647058823529411)
Mn6 of ∈2⅄(φn6/2⅄Qn7)=(1.6/0.894736842105263157)
Mn7 of ∈2⅄(φn7/2⅄Qn8)=(1.625/0.8260869565217391304347)
V= ∈1⅄(Q/φ)cn
The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.
so
V= ∈1⅄(1⅄Qn2/φn1)cn
and
V= ∈1⅄(2⅄Qn2/φn1)cn
then
Vn1 of ∈1⅄(1⅄Qn2/φn1)=(1.6/0)=0
Vn2 of ∈1⅄(1⅄Qn3/φn2)=(1.4/1)=1.4
Vn3 of ∈1⅄(1⅄Qn4/φn3)=(1.571428/2)=0.785714 and Vn3 of ∈1⅄(1⅄Qn4c2/φn3)=(1.571428571428/2)=0.7857140785714
Vn4 of ∈1⅄(1⅄Qn5/φn4)=(1.18/1.5)=0.786 or 0.786666 and so on
Vn5 of ∈1⅄(1⅄Qn6/φn5)=(1.307692/1.6)=0.8173075
Vn6 of ∈1⅄(1⅄Qn7/φn6)=(1.1176470588235294/1.6)=0.698529411764705875
Vn7 of ∈1⅄(1⅄Qn8/φn7)=(1.210526315789473684/1.625)=0.744939271255060728615384
if V= ∈1⅄(1⅄Qn2/φn1)cn
and
V= ∈1⅄(2⅄Qn2/φn1)cn
then
Vn1 of ∈1⅄(2⅄Qn2/φn1)=(0.6/0)=0
Vn2 of ∈1⅄(2⅄Qn3/φn2)=(0.714285/1)=0.714285
Vn3 of ∈1⅄(2⅄Qn4/φn3)=(0.63/2)=0.315
Vn4 of ∈1⅄(2⅄Qn5/φn4)=(0.846153/1.5)=0.564102
Vn5 of ∈1⅄(2⅄Qn6/φn5)=(0.7647058823529411/1.6)=0.4779411764705881875
Vn6 of ∈1⅄(2⅄Qn7/φn6)=(0.894736842105263157/1.6)=0.559210526315789473125
Vn7 of ∈1⅄(2⅄Qn8/φn7)=(0.8260869565217391304347/1.625)=0.5083612040133779264213538461
W=∈2⅄(Q/φ)cn
The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.
so
W=∈2⅄(1⅄Qn1/φn2)cn
and
W=∈2⅄(2⅄Qn1/φn2)cn
then
Wn1 of∈2⅄(1⅄Qn1/φn2)=(1.5/1)=1.5
Wn2 of∈2⅄(1⅄Qn2/φn3)=(1.6/2)=0.8 and Wn2 of∈2⅄(1⅄Qn2c2/φn3)=(1.66/2)=0.88 and so on for cn of Wn2 of∈2⅄(1⅄Qn2/φn3)
Wn3 of∈2⅄(1⅄Qn3/φn4)=(1.4/1.5)=0.93
Wn4 of∈2⅄(1⅄Qn4/φn5)=(1.571428/1.6)=0.9821425 and Wn4 of∈2⅄(1⅄Qn4/φn5c2)=(1.571428/1.66)=0.946643373493975903614457831325301204819277108 and Wn4 of∈2⅄(1⅄Qn4c2/φn5)=(1.571428571428/1.6)=0.9821428571425 and Wn4 of∈2⅄(1⅄Qn4c2/φn5c2)=(1.571428571428/1.66)=0.946643717727710843373493975903614457831325301204819 and so on for cn of Wn4 of∈2⅄(1⅄Qn4cn/φn5cn)
Wn5 of∈2⅄(1⅄Qn5/φn6)=(1.18/1.6)=0.7375
Wn6 of∈2⅄(1⅄Qn6/φn7)=(1.307692/1.625)=0.804733538461
Wn7 of∈2⅄(1⅄Qn7/φn8)=(1.1176470588235294/1.615384)
Wn8 of∈2⅄(1⅄Qn8/φn9)=(1.210526315789473684/1.619047)
if W=∈2⅄(1⅄Qn1/φn2)cn
and
W=∈2⅄(2⅄Qn1/φn2)cn
then
Wn1 of∈2⅄(2⅄Qn1/φn2)=(0.6/1)=0.6
Wn2 of∈2⅄(2⅄Qn2/φn3)=(0.6/2)=0.3
Wn3 of∈2⅄(2⅄Qn3/φn4)=(0.714285/1.5)=0.47619
Wn4 of∈2⅄(2⅄Qn4/φn5)=(0.63/1.6)=0.39375
Wn5 of∈2⅄(2⅄Qn5/φn6)=(0.846153/1.6)=0.528845625
Wn6 of∈2⅄(2⅄Qn6/φn7)=(0.7647058823529411/1.625)=0.4705882352941176
Wn7 of∈2⅄(2⅄Qn7/φn8)=(0.894736842105263157/1.615384)
Wn8 of∈2⅄(2⅄Qn8/φn9)=(0.8260869565217391304347/1.619047)
Then EF and IH paths in wave functions of cycle variants 1⅄, 2⅄, 3⅄
E=∈1⅄(Θ/Q)cn and path ⅄ of Q is a variant in the definition of E
F=∈2⅄(Θ/Q)cn and path ⅄ of Q is a variant in the definition of F
I= ∈1⅄(Q/Θ)cn and path ⅄ of Q is a variant in the definition of I
H=∈2⅄(Q/Θ)cn and path ⅄ of Q is a variant in the definition of H
E=∈1⅄(Θ/Q)cn
The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.
so
E=∈1⅄(Θn2/1⅄Qn1)cn
and
E=∈1⅄(Θn2/2⅄Qn1)cn
then
En1 of 1⅄(Θn2/1⅄Qn1)=(1/1.5)=0.6 or 0.66666
En2 of 1⅄(Θn3/1⅄Qn2)=(0.5/1.6)=0.3125 and
En2 of 1⅄(Θn3/1⅄Qn2c2)=(0.5/1.66)=0.30120481927710843373493975903614457831325 and
En2 of 1⅄(Θn3/1⅄Qn2c3)=(0.5/1.666)=0.30012004801920768307322929171668667466986794717887154861944777911164465786314525810324129651860744297719087635054021608643457382953181272509003601440576230492196878751500600240096038415366146458583433373349339735894357743097238895558223289315726290516206482593037214885954381752701080432172869147659063625450180072028811524609843937575
En3 of 1⅄(Θn4/1⅄Qn3)=(0.6/1.4)=0.428571 and En3 of 1⅄(Θn4c2/1⅄Qn3)=(0.66/1.4)=0.4714285
En4 of 1⅄(Θn5/1⅄Qn4)=(0.6/1.571428)=0.3818183206612075131663684241339724123536044922198153526601282400466327442300888 with an extended shell of decimal having a potential of 1,571,427 total digits in the final quotient based on probability.
En5 of 1⅄(Θn6/1⅄Qn5)=(0.625/1.18)=0.529661016949152542372881355932203389830508474576271186440677
En6 of 1⅄(Θn7/1⅄Qn6)=(0.615384/1.307692)
En7 of 1⅄(Θn8/1⅄Qn7)=(0.619047/1.1176470588235294)
En8 of 1⅄(Θn9/1⅄Qn8)=(0.61764705882352941/1.210526315789473684)
if E=∈1⅄(Θn2/1⅄Qn1)cn
and
E=∈1⅄(Θn2/2⅄Qn1)cn
then
En1 of 1⅄(Θn2/2⅄Qn1)=(1/0.^6)=1.6
En2 of 1⅄(Θn3/2⅄Qn2)=(0.5/0.6)=0.83
En3 of 1⅄(Θn4/2⅄Qn3)=(0.6/0.714285)=0.84000
En4 of 1⅄(Θn5/2⅄Qn4)=(0.6/0.63)=0.95238
En5 of 1⅄(Θn6/2⅄Qn5)=(0.625/0.846153)=0.73863710227346590982954619318255681892045528409164772801136437500
En6 of 1⅄(Θn7/2⅄Qn6)=(0.615384/0.7647058823529411)=0.80473292307692315739636923076923881656000000000
En7 of 1⅄(Θn8/2⅄Qn7)=(0.619047/0.894736842105263157)=0.69187605882352941245658194117647058892717017647058823598599370588235294186834664705882353010364076470588235363305252941176470657422900000000000
En8 of 1⅄(Θn9/2⅄Qn8)=(0.61764705882352941/0.8260869565217391304347)=0.74767801857585139105270634674922600619173684958204334365325075263232662538699690402263165371517027863777068421800309597523219812105337925696594427244368428529411764705882331579695046439628482970000
F=∈2⅄(Θ/Q)cn
The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.
so
F=∈2⅄(Θn1/1⅄Qn2)cn
and
F=∈2⅄(Θn1/2⅄Qn2)cn
then
Fn1 of 2⅄(Θn1/1⅄Qn2)=(0/1.6)=0
Fn2 of 2⅄(Θn2/1⅄Qn3)=(1/1.4)=0.714285
Fn3 of 2⅄(Θn3/1⅄Qn4)=(0.5/1.571428)=0.31818193388433959430530702011164367696133707684984612721677353337219395352507400 with an extended shell of decimal having a potential of 1,571,427 total digits in the final quotient based on probability.
Fn4 of 2⅄(Θn4/1⅄Qn5)=(0.6/1.18)=0.508474576271186440677966101694915254237288135593220338983 for c1 of both variables in equation set Fn4 of 2⅄(Θn4c1/1⅄Qn5c1)
Fn5 of 2⅄(Θn5/1⅄Qn6)=(0.6/1.307692)=0.4588236373702676165335568314251368059145425681276630888 with an extended shell of decimal having a potential of 1,307,691 total digits in the final quotient based on probability.
Fn6 of 2⅄(Θn6/1⅄Qn7)=(0.625/1.1176470588235294)=0.559210526315789479570637119113573469164601253827089149101065829758833148432271892198243667708125181034143870611844010885724953808884325112894250 with an extended shell of decimal having a potential of 11,176,470,588,235,293 total digits in the final quotient based on probability.
Fn7 of 2⅄(Θn7/1⅄Qn8)=(0.615384/1.210526315789473684)=0.5083606956521739131318888166351606805446763159365496835729871853802695101866064670226555669889750377430705333893869630857513971111977327105654603671648230800983409334199692313214505971165163880559044516724376327053746872473804578 with an extended shell of decimal having a potential of 1,210,526,315,789,473,684 total digits in the final quotient based on probability.
if F=∈2⅄(Θn1/1⅄Qn2)cn
and
F=∈2⅄(Θn1/2⅄Qn2)cn
then
Fn1 of 2⅄(Θn1/2⅄Qn2)=(0/0.6)=0
Fn2 of 2⅄(Θn2/2⅄Qn3)=(1/0.714285)=1.40000 or 1.40000140000 and so on...
Fn3 of 2⅄(Θn3/2⅄Qn4)=(0.5/0.63)=0.79365 or 0.79365079365 and so on...
Fn4 of 2⅄(Θn4/2⅄Qn5)=(0.6/0.846153)=0.70909161818252727343636434545525454616363707272798181889090980000
Fn5 of 2⅄(Θn5/2⅄Qn6)=(0.6/0.7647058823529411)=0.78461538461538469384615384615385400000000000000
Fn6 of 2⅄(Θn6/2⅄Qn7)=(0.625/0.894736842105263157)=0.69852941176470588305147058823529411834558823529411764775735294117647058893382352941176470658088235294117647128676470588235294187500000000000000
Fn7 of 2⅄(Θn7/2⅄Qn8)=(0.615384/0.8260869565217391304347)=0.74493852631578947368428502016842105263157895481780631578947368421127125431578947368421060080964210526315789474429149052631578947368495546484210526315789481133595789473684210527060728000000000000000
I= ∈1⅄(Q/Θ)cn
The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.
so
I= ∈1⅄(1⅄Qn2/Θn1)cn
and
I= ∈1⅄(2⅄Qn2/Θn1)cn
then
In1 of 1⅄(1⅄Qn2/Θn1)=(1.6/0)=0
In2 of 1⅄(1⅄Qn3/Θn2)=(1.4/1)=1.4
In3 of 1⅄(1⅄Qn4/Θn3)=(1.571428/0.5)=3.142856
In4 of 1⅄(1⅄Qn5/Θn4)=(1.18/0.6)=1.96 or 1.9666 and so on...
In5 of 1⅄(1⅄Qn6/Θn5)=(1.307692/0.6)=2.179486 or 2.17948666 and so on...
In6 of 1⅄(1⅄Qn7/Θn6)=(1.1176470588235294/0.625)=1.78823529411764704
In7 of 1⅄(1⅄Qn8/Θn7)=(1.210526315789473684/0.615384)=1.9671072302651250016 or 1.9671072302651250016250016250016 and so on...
if I= ∈1⅄(1⅄Qn2/Θn1)cn
and
I= ∈1⅄(2⅄Qn2/Θn1)cn
then
In1 of 1⅄(2⅄Qn2/Θn1)=(0.6/0)=0
In2 of 1⅄(2⅄Qn3/Θn2)=(0.714285/1)=0.714285
In3 of 1⅄(2⅄Qn4/Θn3)=(0.63/0.5)=1.26
In4 of 1⅄(2⅄Qn5/Θn4)=(0.846153/0.6)=1.410255
In5 of 1⅄(2⅄Qn6/Θn5)=(0.7647058823529411/0.6)=1.2745098039215685
In6 of 1⅄(2⅄Qn7/Θn6)=(0.894736842105263157/0.625)=1.4315789473684210512
In7 of 1⅄(2⅄Qn8/Θn7)=(0.8260869565217391304347/0.615384)=1.342392646740472827429214929 or 1.342392646740472827429214929214929214929 and so on...
H=∈2⅄(Q/Θ)cn
The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.
so
H=∈2⅄(1⅄Qn1/Θn2)cn
and
H=∈2⅄(2⅄Qn1/Θn2)cn
then
Hn1 of 2⅄(1⅄Qn1/Θn2)=(1.5/1)=1.5
Hn2 of 2⅄(1⅄Qn2/Θn3)=(1.6/0.5)=3.2 and Hn2 of 2⅄(1⅄Qn2c2/Θn3)=(1.66/0.5)=3.32 and Hn2 of 2⅄(1⅄Qn2c3/Θn3)=(1.666/0.5)=3.332
Hn3 of 2⅄(1⅄Qn3/Θn4)=(1.4/0.^)=2.3 or 2.333 and Hn3 of 2⅄(1⅄Qn3/Θn4)=(1.4/0.66)=2.1 or 21.2121 and so on... for Hn3 of 2⅄(1⅄Qn3/Θn4cn)
Hn4 of 2⅄(1⅄Qn4/Θn5)=(1.571428/0.6)=2.619046 or2.619046 and Hn4 of 2⅄(1⅄Qn4c2/Θn5)=(1.571428571428/0.6)=2.619047619046 or 2.61904761904666 and so on... for Hn4 of 2⅄(1⅄Qn4cn/Θn5)
Hn5 of 2⅄(1⅄Qn5/Θn6)=(1.18/0.625)=1.888 and Hn5 of 2⅄(1⅄Qn5c2/Θn6)=(1.1818/0.625)=1.89088 and Hn5 of 2⅄(1⅄Qn5c3/Θn6)=(1.181818/0.625)=1.8909088 and Hn5 of 2⅄(1⅄Qn5c4/Θn6)=(1.18181818/0.625)=1.890909088 and so on for Hn5 of 2⅄(1⅄Qn5cn/Θn6)
Hn6 of 2⅄(1⅄Qn6/Θn7)=(1.307692/0.615384)=2.1250016 or 2.1250016 and Hn6 of 2⅄(1⅄Qn6c2/Θn7)=(1.307692307692/0.615384)=2.12500 or 2.12500212500 and Hn6 of 2⅄(1⅄Qn6/Θn7c2)=(1.307692/0.615384615384)=2.12499950000 or 2.12499950000212499950000 and Hn6 of 2⅄(1⅄Qn6c2/Θn7c2)=(1.307692307692/0.615384615384)=2.1250000000016 or 2.125000000001621250000000016 and so on for Hn6 of 2⅄(1⅄Qn6cn/Θn7cn)
Hn7 of 2⅄(1⅄Qn7/Θn8)=(1.1176470588235294/0.619047)=1.8054316696850633312171773710235248696787158325619864081402542941004479466017927556389094 or 1.8054316696850633312171773710235248696787158325619864081402542941004479466017927556389094 and
Hn7 of 2⅄(1⅄Qn7/Θn8c2)=(1.1176470588235294/0.619047619047)=1.8054298642551990760181013529221719475067683257936606144796398144606334859683067873321221529411782759990950244298452488705836914027167375375565628913837104090452298642551990760181013529221719475067683257936606144796398144606334859683067873321221529411782759990950244298452488705836914027167375375565628913837104090452 or 1.8054298642551990760181013529221719475067683257936606144796398144606334859683067873321221529411782759990950244298452488705836914027167375375565628913837104090452298642551990760181013529221719475067683257936606144796398144606334859683067873321221529411782759990950244298452488705836914027167375375565628913837104090452298642551990760181013529221719475067683257936606144796398144606334859683067873321221529411782759990950244298452488705836914027167375375565628913837104090452298642551990760181013529221719475067683257936606144796398144606334859683067873321221529411782759990950244298452488705836914027167375375565628913837104090452 and Hn7 of 2⅄(1⅄Qn7c2/Θn8)=(1.11764705882352941176470588235294/0.619047)=1.80543166968506335022172126244524 or 1.80543166968506335022172126244524244524244524 and Hn7 of 2⅄(1⅄Qn7c2/Θn8c2)=(1.11764705882352941176470588235294/0.619047619047)=1.8054298642551990950226262398190 or 1.805429864255199095022626239819002262623981900226262398190 and so on for Hn7 of 2⅄(1⅄Qn7cn/Θn8cn)
Hn8 of 2⅄(1⅄Qn8/Θn9)=(1.210526315789473684/0.61764705882352941)=1.9598997493734335892187611886860007311012224438647639936225403158040876008263056642021550499799209453394906189902503200175922447340485333835968897163291430007530182371308847640562425822787183734940264255582429718876945492140275387267463310876977296954657078696125610346639272465120791466588397519392737523585897674455440543578755260348877743558348362901555457785757227337777498435496840012697614577610019083897946412219102144470323082530768031819970711992670567104678224740963525060985404021800547793291630538477755599880849157555492190135759497777 with an extended shell of decimal having a potential of 61,764,705,882,352,940 total digits in the final quotient based on probability.
then
if H=∈2⅄(1⅄Qn1/Θn2)cn
and
H=∈2⅄(2⅄Qn1/Θn2)cn
then
Hn1 of 2⅄(2⅄Qn1/Θn2)=(0.6/1)=0.6
Hn2 of 2⅄(2⅄Qn2/Θn3)=(0.6/0.5)=1.2
Hn3 of 2⅄(2⅄Qn3/Θn4)=(0.714285/0.6)=1.190475
Hn4 of 2⅄(2⅄Qn4/Θn5)=(0.63/0.6)=1.05
Hn5 of 2⅄(2⅄Qn5/Θn6)=(0.846153/0.625)=1.3538448
Hn6 of 2⅄(2⅄Qn6/Θn7)=(0.7647058823529411/0.615384)=1.2426483014718307593 or 1.2426483014718307593307593307593 and so on...
Hn7 of 2⅄(2⅄Qn7/Θn8)=(0.894736842105263157/0.619047)=1.445345574900230769 or 1.445345574900230769230769 and so on...
Hn8 of 2⅄(2⅄Qn8/Θn9)=(0.8260869565217391304347/0.61764705882352941)=1.337474120082815738810868914522330682316768327206659092333623792019025978096067977197217080274479934849191657927085528140547594077387223258707411649677780739164033284793659254754380813696169299298230896274769426566373989356484075903925683875668788 with an extended shell of decimal having a potential of 61,764,705,882,352,940 total digits in the final quotient based on probability.
And so on for function set H=∈2⅄(Q/Θ)cn
Then DB and OG paths in wave functions of cycle variants 1⅄, 2⅄, 3⅄
Variables of set ∈3⅄φ/Θ=(φn1cn/Θn1cn) differ from D and B sets
D=∈1⅄(φ/Θ)cn
B=∈2⅄(φ/Θ)cn
O=∈1⅄(Θ/φ)cn
G=∈2⅄(Θ/φ)cn
Variables of set ∈3⅄Θ/φ=(Θn1cn/φn1cn) differ from O and G sets
IF D=∈1⅄(φn2/Θn1)cn
then
D=∈1⅄(φn2/Θn1)cn
Dn1=(φn2/Θn1)=(1/0)=0
Dn2=(φn3/Θn2)=(2/1)=2
Dn3=(φn4/Θn3)=(1.5/0.5)=3
Dn4=(φn5/Θn4)=(1.6/0.6) ↓ and Dn4=(φn5c2/Θn4)=(1.66/0.6) and Dn4=(φn5/Θn4c2)=(1.6/0.66) and Dn4=(φn5c2/Θn4c2)=(1.66/0.66) and so on for cn
Dn5=(φn6/Θn5)=(1.6/0.6)=2.6 or 2.6 or 2.66 or 2.666 and so on
Dn6=(φn7/Θn6)=(1.625/0.625)=2.6
Dn7=(φn8/Θn7)=(1.615384/0.615384)=2.625001 or 2.625001
Dn8=(φn9/Θn8)=(1.619047/0.619047)=2.615386230770846155461540076924692309307693923078538463153847769232384617000001 or 2.615386230770846155461540076924692309307693923078538463153847769232384617000001
Dn9=(φn10/Θn9)=(1.61762941/0.61764705882352941) with a quotient potential of 61,764,705,882,352,941 digits long to divisor of cn of variable Θn9 of Dn9 and Dn8=(φn9c1/Θn8c2), Dn8=(φn9c2/Θn8c2) each have quotients based on cn of Dn variables φncn/Θncn
Dn10=(φn11/Θn10)=(1.618/0.618)=2.6181229773462783171521035598705501 or 2.6181229773462783171521035598705501
Dn11=(φn12/Θn11)=(1.61797752808988764044943820224719101123595505/0.6179775280878651685393258764044943820224719101123595505)
Dn12=(φn13/Θn12)=(1.6180^5/0.6180^5)
Dn13=(φn14/Θn13)=(1.61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832/0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566)
Dn14=(φn15/Θn14)=(1.61830223896551724135014/0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257)
Dn15=(φn16/Θn15)=(1.618032786885245901639344262295081967213114754098360655737704918/0.618032786885245901639344262295081967213114754098360655737749)
Dn16=(φn17/Θn16)=(1.6180344478216818642350572441742654508601925025329280648429584599797365754812563323201418439716312056737588652482269503546099290780141843/0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870)
Dn17=(φn18/Θn17)=(1.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/0.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129)
Dn18=(φn19/Θn18)=(1.618034055731424148606811145510835913312693/0.618034055727554179566563467492260061919504643962848297213622291021671826625386996904024767801857585139318885448916408668730650154798761609907120743)
Dn19=(φn20/Θn19)=(1.61803396316670629036115761779478593637885673283903372398947620186558239655584788327911265247548433389141353743123654628079406840468787371442238722793590050227218368811289165271466156421908634298014828988280315713944032525711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242/0.618033963166706529538387945467591485290600334848122458741927768476441042812724228653432193255202104759626883520688830423343697679980865821573786175556087060511839272901219803874671131308299449892370246352547237502989715379095910069361396795025113609184405644582635733078210954317149007414494140157856972016264051662281750777325998564936)
Dn20=(φn21/Θn20)=(1.61803399852/0.61803399852)
Dn21=(φn22/Θn21)=(1.6180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981/0.6180339850173579389731408733784030696144710396491869175954686643522748035812168828795907180705280467750776539375114196966928558377489493879042572629270966563128083318107071076192216334734149460990316097204458249588890919057189841037822035446738534624520372738900054814544125708021194957061940434862050063950301479992691394116572263840672391741275351726658139959802667641147451123698154577014434496619769778914672026310981)
Dn22=(φn23/Θn22)=(1.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793292304217717802495624188357517983174298458585060132121280560103890237705381401388967308452374230704082208796792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869/0.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793348766303427248602563378691208853255039241149568065044322737281915193947264411947377336118796228332674609000056462085709446106939190333690926542826492010614872113375868104567782733894190051380497995595957314663203658743153972107729659533623172039975156682287843712946756253175992321156343515329456270114)
and so on for ∈Dn=1⅄(φ/Θ)ncn equations beyond Dn22 that differs from equations such as ∈Dn1of 1⅄(2φn2/2Θn1)ncn or ∈Dn1of 1⅄(1φn2/2Θn1)ncn and ∈Dn1of 1⅄(2φn2/1Θn1)ncn of ∈1⅄ᐱD(nφncn/nΘncn) sets
IF B=∈2⅄(φn1/Θn2)cn
then
Bn1=(φn1/Θn2)=(0/1)=0
Bn2=(φn2/Θn3)=(1/0.5)=2
Bn3=(φn3/Θn4)=(2/0.6)=3.33333 and Bn3=(φn3/Θn4c2)=(2/0.66) and Bn3=(φn3/Θn4c3)=(2/0.666) and so on for variants of ncn
Bn4=(φn4/Θn5)=(1.5/0.6)=2.5
Bn5=(φn5/Θn6)=(1.6/0.625)=2.56
Bn6=(φn6/Θn7)=(1.6/0.615384)=2.60000 or 2.60000260000 and so on...
Bn7=(φn7/Θn8)=(1.625/0.619047)=2.62500 or 2.62500262500
Bn8=(φn8/Θn9)=(1.615384/0.61764705882352941)=2.61538361904761905509157224489795920502353974732750249054344689712619759202889589655104073913017875205059258799098691062074072759329593510687826931417886221012838851670151107655730052390907926635419 and many more digits longer probability... given the denominator and numerator with a calculated limit of a 61,764,705,882,352,941 -1 minus one digits to its quotient at repeated sequence decimals digits.
Bn9=(φn9/Θn10)=(1.619047/0.618)=2.61981715210355987055016181229773462783 or 2.61981715210355987055016181229773462783
Bn10=(φn10/Θn11)=(1.61762941/0.6179775280878651685393258764044943820224719101123595505)
Bn11=(φn11/Θn12)=(1.618/0.61805)
Bn12=(φn12/Θn13)=(1.61797752808988764044943820224719101123595505/0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566)
Bn13=(φn13/Θn14)=(1.61805/0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257)
Bn14=(φn14/Θn15)=(1.61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832/0.618032786885245901639344262295081967213114754098360655737749)
Bn15=(φn15/Θn16)=(1.61830223896551724135014/0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870)
Bn16=(φn16/Θn17)=(1.618032786885245901639344262295081967213114754098360655737704918/0.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129)
Bn17=(φn17/Θn18)=(1.6180344478216818642350572441742654508601925025329280648429584599797365754812563323201418439716312056737588652482269503546099290780141843/0.618034055727554179566563467492260061919504643962848297213622291021671826625386996904024767801857585139318885448916408668730650154798761609907120743)
Bn18=(φn18/Θn19)=(1.6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/0.618033963166706529538387945467591485290600334848122458741927768476441042812724228653432193255202104759626883520688830423343697679980865821573786175556087060511839272901219803874671131308299449892370246352547237502989715379095910069361396795025113609184405644582635733078210954317149007414494140157856972016264051662281750777325998564936)
Bn19=(φn19/Θn20)=(1.618034055731424148606811145510835913312693/0.61803399852)
Bn20=(φn20/Θn21)=(1.61803396316670629036115761779478593637885673283903372398947620186558239655584788327911265247548433389141353743123654628079406840468787371442238722793590050227218368811289165271466156421908634298014828988280315713944032525711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242/0.6180339850173579389731408733784030696144710396491869175954686643522748035812168828795907180705280467750776539375114196966928558377489493879042572629270966563128083318107071076192216334734149460990316097204458249588890919057189841037822035446738534624520372738900054814544125708021194957061940434862050063950301479992691394116572263840672391741275351726658139959802667641147451123698154577014434496619769778914672026310981)
Bn21=(φn21/Θn22)=(1.61803399852/0.618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793348766303427248602563378691208853255039241149568065044322737281915193947264411947377336118796228332674609000056462085709446106939190333690926542826492010614872113375868104567782733894190051380497995595957314663203658743153972107729659533623172039975156682287843712946756253175992321156343515329456270114)
and so on for ∈Bn1=2⅄(φn1/Θn2)ncn equations beyond Bn21 that differs from equations such as ∈Bn1of 2⅄(2φn1/2Θn2)ncn or ∈Bn1of 2⅄(1φn1/2Θn2)ncn and ∈Bn1of 2⅄(2φn1/1Θn2)ncn of ∈2⅄ᐱB(nφncn/nΘncn) sets
IF O=∈1⅄(Θn2/φn1)cn
On1=(Θn2/φn1)=(1/0)=0
On2=(Θn3/φn2)=(0.5/1)=0.5
On3=(Θn4/φn3)=(0.6/2)=0.3 and On3=(Θn4c2/φn3)=(0.66/2)=0.33 and On3=(Θn4c3/φn3)=(0.666/2)=0.333 and so on for variants of ncn
On4=(Θn5/φn4)=(0.6/1.5)=0.4
On5=(Θn6/φn5)=(0.625/1.6)=0.390625 and On5=(Θn6/φn5c2)=(0.625/1.66)=0.3765060240963855421686746987951807228915662 or 0.3765060240963855421686746987951807228915662 and so on for variants of ncn
On6=(Θn7/φn6)=(0.615384/1.6)=0.384615 and On6=(Θn7c2/φn6)=(0.615384615384/1.6)=0.384615384615 and so on for variants of ncn
On7=(Θn8/φn7)=(0.619047/1.625)=0.380952
On8=(Θn9/φn8)=(0.61764705882352941/1.615384)=0.38235308683478938134833575174695304645830341268701435695785026965724558371260331908697869980140944 with an extended shell of decimal having a potential of 1,615,383 total digits in the final quotient based on probability.
On9=(Θn10/φn9)=(0.618/1.619047)=0.3817060282993637615214382287852051237549002592265697042766516351903311021854214238376032320247 with an extended shell of decimal having a potential of 1,619,046 total digits in the final quotient based on probability.
On10=(Θn11/φn10)=(0.6179775280878651685393258764044943820224719101123595505/1.61762941)=0.3820266398889626818415262840729969060234086063707011549079093461833140138074022776329221165680957 with an extended shell of decimal having a potential of 161,762,940 total digits in the final quotient based on probability.
On11=(Θn12/φn11)=(0.61805/1.618)=0.3819839307787391841779975278121137206427688504326328800988875154511742892459826946847960444993819530284301606922126081582200247218788627935723114956736711990111248454882571075401730531520395550061804697156 or 0.3819839307787391841779975278121137206427688504326328800988875154511742892459826946847960444993819530284301606922126081582200247218788627935723114956736711990111248454882571075401730531520395550061804697156
On12=(Θn13/φn12)=(0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566/1.61797752808988764044943820224719101123595505)
On13=(Θn14/φn13)=(0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/1.61805)
On14=(Θn15/φn14)=(0.618032786885245901639344262295081967213114754098360655737749/1.61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832)
On15=(Θn16/φn15)=(0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870/1.61830223896551724135014)
and so on for ∈On=1⅄(Θ/φ)cn
IF G=∈2⅄(Θn1/φn2)cn
G=∈2⅄(Θn1/φn2)cn
Gn1=(Θn1/φn2)=(0/1)=0
Gn2=(Θn2/φn3)=(1/2)=0.5
Gn3=(Θn3/φn4)=(0.5/1.5)=0.3 or 0.3333 and so on...
Gn4=(Θn4/φn5)=(0.6/1.6)=0.375 and Gn4=(Θn4c2/φn5)=(0.66/1.6)=0.4125 and Gn4=(Θn4/φn5c2)=(0.6/1.66)=0.3614457831325301204819277108433734939759 and
Gn4=(Θn4c2/φn5c2)=(0.66/1.66)=0.39759036144578313253012048192771084337349 or 0.39759036144578313253012048192771084337349 and so on for variants of set ∈Gn4=(Θn4cn/φn5cn)ncn
Gn5=(Θn5/φn6)=(0.6/1.6)=0.375
Gn6=(Θn6/φn7)=(0.625/1.625)=0.384615 or 0.384615
Gn7=(Θn7/φn8)=(0.615384/1.615384)=0.38095214512462671414351014990862853662039490300758209812651357200517028768391911768347340322796313446214646177 with an extended shell of decimal having a potential of 1,615,383 total digits in the final quotient based on probability.
Gn8=(Θn8/φn9)=(0.619047/1.619047)=0.3823527050172107418746954226776616120470869591803079218824407197567457893439782785799300452673702 with an extended shell of decimal having a potential of 1,619,046 total digits in the final quotient based on probability.
Gn9=(Θn9/φn10)=(0.61764705882352941/1.61762941)=0.3818223475694160444325749492895285577182971716618332254480956797144285352724886474461415733 with an extended shell of decimal having a potential of 161,762,940 total digits in the final quotient based on probability.
Gn10=(Θn10/φn11)=(0.618/1.618)=0.3819530284301606922126081582200247218788627935723114956736711990111248454882571075401730531520395550061804697156983930778739184177997527812113720642768850432632880098887515451174289245982694684796044499
Gn11=(Θn11/φn12)=(0.6179775280878651685393258764044943820224719101123595505/1.61797752808988764044943820224719101123595505)=0.38194444444319444444444446527777777777777777923659336415456211419753094376929012345679012902865 with an extended shell of decimal having a potential of 161,797,752,808,988,764,044,943,820,224,719,101,123,595,504 total digits in the final quotient based on probability.
Gn12=(Θn12/φn13)=(0.61805/1.61805)=0.381972126942925125923179135379005593152251166527610395228824819999 or 0.381972126942925125923179135379005593152251166527610395228824819999
Gn13=(Θn13/φn14)=(0.618025755364806437768240343347639484978540772532206008583690987124463519313304721030042918454935622317596566/1.61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832)
Gn14=(Θn14/φn15)=(0.610079575596814323607427055702917771827585941644562334217506631294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/1.61830223896551724135014)
Gn15=(Θn15/φn16)=(0.618032786885245901639344262295081967213114754098360655737749/1.618032786885245901639344262295081967213114754098360655737704918)
Gn16=(Θn16/φn17)=(0.618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870/1.6180344478216818642350572441742654508601925025329280648429584599797365754812563323201418439716312056737588652482269503546099290780141843)
and so on for ∈Gn=2⅄(Θ/φ)ncn
Then LK and UJ paths in wave functions of cycle variants 1⅄, 2⅄, 3⅄
L=∈1⅄(1⅄Qn2/2⅄Qn1)cn
K=∈2⅄(1⅄Qn1/2⅄Qn2)cn
U=∈1⅄(2⅄Qn2/1⅄Qn1)cn
J=∈2⅄(2⅄Qn1/1⅄Qn2)cn
Given L=∈1⅄(1⅄Qn2/2⅄Qn1)cn
∈1⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn2/2⅄1Qn1)=(1.6/0.6)=2.6 depending of cn variable factor c1
then
Ln1=∈1⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn2/2⅄1Qn1)=(1.6/0.6)=2.6 or 2.666 and so on...
Ln2=∈1⅄2Qn2 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn3/2⅄1Qn2)=(1.4/0.6)=2.3 or 2.333 and so on...
Ln3=∈1⅄2Qn3 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn4/2⅄1Qn3)=(1.571428/0.714285)=2.2000014 or 2.2000014000014000014 and so on...
Ln4=∈1⅄2Qn4 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn5/2⅄1Qn4)=(1.18/0.63)=1.873015 or 1.873015873015873015 and so on...
Ln5=∈1⅄2Qn5 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn6/2⅄1Qn5)=(1.307692/0.846153)=1.545455727273909092090910272728454546636364818183000001181819363637 or 1.545455727273909092090910272728454546636364818183000001181819363637545455727273909092090910272728454546636364818183000001181819363637545455727273909092090910272728454546636364818183000001181819363637 and so on...
Ln6=∈1⅄2Qn6 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn7/2⅄1Qn6)=(1.1176470588235294/0.7647058823529411)=1.461538461538461669230769230769243846153846153847 or 1.461538461538461669230769230769243846153846153847461538461538461669230769230769243846153846153847461538461538461669230769230769243846153846153847 and so on...
Ln7=∈1⅄2Qn7 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn8/2⅄1Qn7)=(1.210526315789473684/0.894736842105263157)=1.352941176470588236411764705882352942294117647058823530529411764705882354058823529411764707000000000000000001117647058823529412882352941176470589 or 1.352941176470588236411764705882352942294117647058823530529411764705882354058823529411764707000000000000000001117647058823529412882352941176470589352941176470588236411764705882352942294117647058823530529411764705882354058823529411764707000000000000000001117647058823529412882352941176470589352941176470588236411764705882352942294117647058823530529411764705882354058823529411764707000000000000000001117647058823529412882352941176470589 and so on...
Variable Factor 1⅄2Qnc1 will differ variants of ∈1⅄2Qn given a factor 1⅄1Qnc2 factor 2⅄1Qnc2 and so on . . .
Given K=∈2⅄(1⅄Qn1/2⅄Qn2)cn
∈2⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn1/2⅄1Qn2)=(1.5/0.6) depending of cn variable factor
then
Kn1=∈2⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn1/2⅄1Qn2)=(1.5/0.6)=2.5
Kn2=∈2⅄2Qn2 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn2/2⅄1Qn3)=(1.6/0.714285)=2.24000 or 2.24000224000 and so on...
Kn3=∈2⅄2Qn3 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn3/2⅄1Qn4)=(1.4/0.63)=2.22 or 2.222222 and so on...
Kn4=∈2⅄2Qn4 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn4/2⅄1Qn5)=(1.571428/0.846153)=1.857144038962220780402598584416766234948053129871311689493507675325 or 1.857144038962220780402598584416766234948053129871311689493507675325857144038962220780402598584416766234948053129871311689493507675325 and so on...
Kn5=∈2⅄2Qn5 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn5/2⅄1Qn6)=(1.^1/0.7647058823529411)=1.54307692307692323123076923076924620000000000000 or 1.54307692307692323123076923076924620000000000000154307692307692323123076923076924620000000000000 and so on...
Kn6=∈2⅄2Qn6 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn6/2⅄1Qn7)=(1.307692/0.894736842105263157)=1.46153811764705882499094988235294117793212635294117647204977341176470588381447929411764706028506752941176470734389105882352941322624400000000000 or 1.46153811764705882499094988235294117793212635294117647204977341176470588381447929411764706028506752941176470734389105882352941322624400000000000146153811764705882499094988235294117793212635294117647204977341176470588381447929411764706028506752941176470734389105882352941322624400000000000 and so on...
Kn7=∈2⅄2Qn7 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn7/2⅄1Qn8)=(1.1176470588235294/0.8260869565217391304347)=1.35294117647058822105276687306501547987473685563467492260061905263293188854489164085263171424148606811145368422405572755417956642105398452012383900927368434582043343653250631580300309597523219800000 or 1.35294117647058822105276687306501547987473685563467492260061905263293188854489164085263171424148606811145368422405572755417956642105398452012383900927368434582043343653250631580300309597523219800000135294117647058822105276687306501547987473685563467492260061905263293188854489164085263171424148606811145368422405572755417956642105398452012383900927368434582043343653250631580300309597523219800000 and so on....
Variable Factor 2⅄2Qnc1 will differ variants of ∈1⅄1Qn and ∈2⅄1Qn given a factor 1⅄1Qnc2 factor 2⅄1Qnc2 and so on . . .
Given U=∈1⅄(2⅄Qn2/1⅄Qn1)cn
∈1⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn2/1⅄1Qn1)=(0.6/1.5)=0.4
then
Un1=∈1⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn2/1⅄1Qn1)=(0.6/1.5)=0.4
Un2=∈1⅄2Qn2 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn3/1⅄1Qn2)=(0.714285/1.6)=0.446428125
Un3=∈1⅄2Qn3 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn4/1⅄1Qn3)=(0.63/1.4)=0.45
Un4=∈1⅄2Qn4 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn5/1⅄1Qn4)=(0.846153/1.571428)=0.538461195804071201480436901977055264383732503175455700165709151166964060714203896074144026961464349623399863054495656180238610995858543948561435840522123826226 with an extended shell of decimal having a potential of 1,571,427 total digits in the final quotient based on probability.
Un5=∈1⅄2Qn5 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn6/1⅄1Qn5)=(0.7647058823529411/1.18)=0.6480558325024924576271186440677966101694915254237288135593220338983050847 or 0.6480558325024924576271186440677966101694915254237288135593220338983050847
Un6=∈1⅄2Qn6 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn7/1⅄1Qn6)=(0.894736842105263157/1.307692)=0.68421068730653942747986528938006808942778574771429357983378349030199771811711 with an extended shell of decimal having a potential of 1,307,691 total digits in the final quotient based on probability.
Un7=∈1⅄2Qn7 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn8/1⅄1Qn7)=(0.8260869565217391304347/1.1176470588235294)=0.7391304347826087034324203661327231940254775382391915160576582972546 with an extended shell of decimal having a potential of 11,176,470,588,235,293 total digits in the final quotient based on probability.
Variable Factor 1⅄2Qnc1 will differ variants of ∈2⅄1Qn and ∈1⅄1Qn given a factor 1⅄1Qnc2 factor 2⅄1Qnc2 and so on . . .
Given J=∈2⅄(2⅄Qn1/1⅄Qn2)cn
∈2⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn1/1⅄1Qn2)=(0.6/1.6)
depending of cn variable factor and are crossed variants of two different path sets variables
then
Jn1=∈2⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn1/1⅄1Qn2)=(0.6/1.6)=0.375
Jn2=∈2⅄2Qn2 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn2/1⅄1Qn3)=(0.6/1.4)=0.428571 or 0.428571428571 and so on...
Jn3=∈2⅄2Qn3 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn3/1⅄1Qn4)=(0.714285/1.571428)=0.45454516528915101423673244972089080759665730787538468195806616656951511618731497720544625652591146396780507920184698248981181447702344619034406921602516946369798679926792700651891146 with an extended shell of decimal having a potential of 1,571,427 total digits in the final quotient based on probability.
Jn4=∈2⅄2Qn4 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn4/1⅄1Qn5)=(0.^6/1.18)=0.533898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220 or 0.53389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220 and so on...
Jn5=∈2⅄2Qn5 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn5/1⅄1Qn6)=(0.846153/1.307692)=0.6470583287196067575545311893014563062250132294148775093829433842219727581112372026440476809523955182107101672259217002168706392636798267481945289869479969 with an extended shell of decimal having a potential of 1,307,691 total digits in the final quotient based on probability.
Jn6=∈2⅄2Qn6 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn6/1⅄1Qn7)=(0.7647058823529411/1.1176470588235294)=0.684210526315789412465373961218835920688146960198272849348915370508135256304372321138265855835498117244903745636822286788460480387603018825899 with an extended shell of decimal having a potential of 11,176,470,588,235,293 total digits in the final quotient based on probability.
Jn7=∈2⅄2Qn7 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn7/1⅄1Qn8)=(0.894736842105263157/1.210526315789473684)=0.73913043478260869504158790170132325131158050464370839153244878341629711157086065798544297592536707095399008276962905581808523178602244449010177944104738165045248338105171854790477971844377713876604864668587428500279106898884770173961583808501699160688971097130730288815473234283605267620082301614540046542623008976441747224804001561120303865183304619325270237423183412056568736943162332531577171642289101309839508111 with an extended shell of decimal having a potential of 1,210,526,315,789,473,683 total digits in the final quotient based on probability.
Variable Factor 2⅄2Qnc1 will differ variants of ∈2⅄1Qn and ∈1⅄1Qn given a factor 1⅄1Qnc2 factor 2⅄1Qnc2 and so on . . .
Then RZ and TS paths in wave functions of cycle variants
R=∈(φ/P)cn that paths 1⅄, 2⅄, 3⅄ are then applicable to the variables φ and P of ∈R
Z=∈(P/φ)cn that paths 1⅄, 2⅄, 3⅄ are then applicable to the variables P and φ of ∈Z
T=∈(Θ/P)cn that paths 1⅄, 2⅄, 3⅄ are then applicable to the variables Θ and P of ∈T
S=∈(P/Θ)cn that paths 1⅄, 2⅄, 3⅄ are then applicable to the variables Θ and P of ∈S
Phi Prime
R=∈(φ/P)cn
Given R=∈(φ/P)cn
R represents ∈(φ/P)cn
3⅄φncn/pn that path 3⅄ of φncn/pn differ from paths 2⅄φncn/pn and 1⅄φncn/pn
Path 3⅄R=φn1cn/pn1
3⅄Rn1=1φn1/pn1=(φn1/pn1)=(0/2)=0
3⅄Rn2=1φn2/pn2=∈(φn2/pn2)=(1/3)=0.3
3⅄Rn3=1φn3/pn3=(φn3/pn3)=(2/5)=0.4
3⅄Rn4=1φn4/pn4=∈(φn4/pn4)=(1.5/7)=0.2142857
3⅄Rn5=1φn5/pn5=∈(φn5/pn5)=(1.6/11)=1.45→. . .(φn5c2/pn5)=(1.66/11)=0.1509→. . . and so on
3⅄Rn6=1φn6/pn6=∈(φn6/pn6)=(1.6/13)=0.1230769
3⅄Rn7=1φn7/pn7=∈(φn7/pn7)=(1.625/17)=0.0955882352941176470
3⅄Rn8=1φn8/pn8=∈(φn8/pn8)=(1.615384/19)=0.079757052631578421→. . .(φn8c2/pn8)=(1.615384615384/19)=0.079757079757052631578421→. . . and so on
3⅄Rn9=1φn9/pn9=∈(φn9/pn9)=(1.619047/23)=0.0703933478260865217391304
Path 1⅄R=φn2/pn1
1⅄Rn1=(φn2/pn1)=(1/2)=0.5
1⅄Rn2=(φn3/pn2)=(2/3)=0.6 or 0.666 and so on...
1⅄Rn3=(φn4/pn3)=(1.5/5)=0.3
1⅄Rn4=(φn5/pn4)=(1.6/7)=0.2285714 or 0.2285714285714285714 and so on...
1⅄Rn5=(φn6/pn5)=(1.6/11)=0.145 or 0.1454545 and so on...
1⅄Rn6=(φn7/pn6)=(1.625/13)=0.125
1⅄Rn7=(φn8/pn7)=(1.615384/17)=0.0950225882352941176470 or 0.095022588235294117647058823529411764705882352941176470 and so on...
1⅄Rn8=(φn9/pn8)=(1.619047/19)=0.085213 and 1⅄Rn8=(φn9c2/pn8)=(1.619047619047/19)=0.085213032581421052631578947368 or 0.085213032581421052631578947368421052631578947368 and so on for cn of 1⅄Rn8=(φn9cn/pn8)
1⅄Rn9=(φn10/pn9)=(1.61762941/23)=0.070331713478260869565217391304 or 0.0703317134782608695652173913043478260869565217391304 and so on....
Path 2⅄R=φn1/pn2
2⅄Rn1=(φn1/pn2)=(0/3)=0
2⅄Rn2=(φn2/pn3)=(1/5)=0.2
2⅄Rn3=(φn3/pn4)=(2/7)=0.285714 or 0.285714285714285714 and so on....
2⅄Rn4=(φn4/pn5)=(1.5/11)=0.136 or 0.1363636 and so on...
2⅄Rn5=(φn5/pn6)=(1.6/13)=0.1230769 or 0.1230769230769230769 and so on....
2⅄Rn6=(φn6/pn7)=(1.6/17)=0.09411764705882352 or 0.0941176470588235294117647058823529411764705882352 and so on...
2⅄Rn7=(φn7/pn8)=(1.625/19)=0.085526315789473684210 or 0.085526315789473684210526315789473684210526315789473684210 and so on....
2⅄Rn8=(φn8/pn9)=(1.615384/23)=0.0702340869565217391304347826 or 0.070234086956521739130434782608695652173913043478260869565217391304347826 and so on...
Variable Differential ratio scale of divisor and dividend to applicable cycle shell phi prime to prime phi and comparable quotient sets.
Z=∈(P/φ)cn
Z represents ∈(P/φ)cn
3⅄p/φncn that path 3⅄ of p/φncn differ from paths 2⅄p/φncn and 1⅄p/φncn
3⅄Zn1=pn1/φn1=(pn1/φn1)=(2/0)=0
3⅄Zn2=pn2/φn2=(pn2/φn2)=(3//1)=3
3⅄Zn3=pn3/φn3=(pn3/φn3)=(5/2)=2.5
3⅄Zn4=pn4/φn4=(pn4/φn4)=(7/.1.5)=4
3⅄Zn5=pn5/φn5=∈(pn5/φn5)=(11/1.6)=6.875 →. . .(pn5/φn5c2)=(11/1.66)=6.626506024096084337349397590361445784337951712047→. . . and so on
3⅄Zn6=pn6/φn6=(pn6/φn6)=(13/1.6)=8.125
3⅄Zn7=pn7/φn7=∈(pn7/φn7)=(17/1.625)=10.4615076923
3⅄Zn8=pn8/φn8=∈(pn8/φn8)=(19/1.615384)= 11.7619924287971155465202081053173734542375063761929052163510348003942096739846377084334127365385567765992482282850393466816496882475006561907261678956830078792410968537573691456644 extended shell 588704/1615384 →. . . then (pn8/φn8c2)=(19/1.615384615384)→. . . and so on
3⅄Zn9=pn9/φn9=∈(pn9/φn9)=(23/1.619047)=14.2058877846041529368820052784137829229169999388529177967038634455948468450884995926616089588504842663616312559178331450538495794130744814696546795738480723536747234638648538306794058480081183560452537820087990033643248157712530890085340326747771991795173333448627495063453994850056854433503165751210434286342521248611065645407452655790721331746391550090886799456717439333138568552982093787271153956617689294998848087794857098033596306963293838906467817178871274274310751942346330897126519489551569534423645514923285117726662660194546544973678960524308435764990145437408549597386610765468822091020211272433721812893634341683718879068983173434742783872240892327400007535296998790028949128715843332528333025539098000243353034223218967701370003465001324853447738082958678778318356415842158998472558239507562164656121780281857166592446050052901490815275899958432337047658282928167001946206626490768952352834723142688260439628991622849738148429292046494017777124444194640427362516344491543482060743140872377392379591203961342691101617185912453437114549484974803078601177112214778199768135205463460912499760661673194169162476444476287593874668246196682369319729445778905738993370791582949722892541105971599342082101384332882244925564236245149152557028918863998389175854684885614809205662343341484218802789542243060269405397125593018609095350536457558057301610144733290633317006856502621603943554449006112855278444665287666139401759183025569980364992492497129484196567486922862646976894432341988836642790481066948643245069476055976139049700224885380103233568883423396603063407053655638162449885642603333936568858099857508769047470518150492234011736533899262961482897037578279074047881253601655788868389861443182316510885724750424169279829430523017552918476115887926663030782923534647233835707054829168022917185233041412633481301036968043546604885466573854866473919534145704232181029951570275600399494270394868092155447000612088469327944154802176836126437342461336823452314849414501246721064922760117525927289325140036082954972894548459680293407171008624209179844686411203627813151810910986524788965360486755480230036558543390031296188436777931709209182932922886117574103778333797598216728729925690853940620624354944606302349468545385032058982846081676442993934085915974026695951383746117314691914441026109804100807450308731000397147210673933492974570843218263583453723085247062006229590617196412457451821966873104980893080929707414299893702900533461968676635082242825563433303665674930993355968047870135950346098661743605960790514419902572315689414822423314455973174342684307496941101771597736199134429080811119133663198165340474983122787664595283521726052424667103549186651159601913965437692667353078693824206462196588486930892061811670692697617796147980880110336512775725473071504409692862529623908385612029792834920789822654932191591720314481296713436978667080078589441813610105203863754418494336483128655313897620019678242818151665763872203833489701040179809480515389608825438668550079151500852044443428757781583857664416165806181043539810765221763173027095569183599981964698986502553662741106342187719071774939208064991318967269016896977048844165734533957321807211279227842057704316181062069229614705440916786232888853751620552090211093316006267884749485345391455590850667089960946161538238235208736991575908543729737308428970869900626726710219036260219746554608976762255820862519741551665887401662830047552665240724944983067199408046832488494775012708093094270888985928141678407112332131185814865164507268782191004955384247646918217939318623857120886546221326496389542737178105391628532093262270953221246819888489957363807227338057511610225027438981079610412792216655847544882884808161838414820570372571024806568308393764974086607738997076675352846458441292933435533372409818862577800397394269591926608677820965049192518808904250463389883060837640908509759136084375561673008874973981607698850002501471544680296495407483538155470471209297815319752916376115084985179553156887971751283316667150490381069851585531488585569165070563115215308758794525421436190549131680550348445721464540559971390577296397201563635891978429285870021067949231862941594654139132464962413073863822359696784589947049097401125476900917638586155930000796765010527798142981642904745816520459257822657402780771651471513797931746268020631890241605092378417674100875391511179107215540994177438950197245663652753749582316016767888764192762779585768665146842556145683232173000536735499340043865310889677693112059131081432472312415884159014531387909060082875914040790662655253368185111364895521871817186283041814104223039849985824994580144986526024259950452333996480645713188066807202014518417315865444301493409394538886147221173937507681988231348441397933475680446583700164355945194920221587143548025474245034270160162120061987082524472729945455567380069880614954352776664296959878249365212992581438339961718220656966721781393622297561466714678449729995484998273675810523104023539773706384064205671608050908960641661421811720104481216419288630904476522299846761706114769985059111934366327845948882274572634395419033542571648630336241010915680644230834558848507795017686330291832170406418096571625159739031664923871882656896309989765584322135181992863703153768852911620230913617702265592042726369277729429720076069440850080325030712511743019195860280770107353276340958600954759188584395635210095815624870680097612978499080014354123135400022358832078376971144136025699068649643895452077672853227855645944805802425747986315406532361321196975751784846270676515258667598902317227356586930459708705182740216930082943855243238769473647151688616822118196692251676449170407035743866607948997156969501194221044849223030585276400252741273106957364424874633040300868350332016303417998365705257475539623000444088405092625476592093991094761300938144476349358604166525122494899777461679617701030297452760790761478820565431392664944254243391328355507900635373772348795309833500818691489499687161645091217240759533231586235606501849544824825962433456224556791742302724998100734567927923031264688424733809457044792399479446859788505213251993302232733206633284889197163516562521038610985351259104893187165042151339646100452920761410879362983285846550470739885871132833080200883606220202378312674060728317337297805437396196651486954980306315999473764504674663552077240500121367693464118089221622349443839493232747412521069493350100398567799452393908268259043746104961746014785240947298009261003540971942136330816832371141788965978134050463019294683847967353634576389690972528901261050482166360828314434355519018286683462555441565315892620782472652121896399548623356826577610162027414892835106084011149768969029311687677998229822852579325986212877081394178180126951225010762504115075102822833432259841746410079509736283134461198470458238704620681178495744718961216073406145714114537749676198405605272731427809075338764100115685338350276428046869547332473980063580612545528326231418853189561513655872868421979102521421552308240588444930876002982001140176906538228970499312249737036664161077473353151576205014431329047272871016097741449136436434519813198752105405216772582883634631977947520979934492327894125371283230196529192790573714042890663458194851662737400458417822336226187380601057288639551538652058896375460378852497796543275148899321637975920402557800977982726875748511315607267732190603484642508833900436491343364337168717152744793696538766323645947276391605679143347907750670610550527563437009549444827728904719875334069980673816139988524113259219775584031840953350952751834875701570121188575748573080336766011116416015100241067739231782647446306376528908672818021959831925818089283387078942118419045277870253303332145391702649768660205664196283369167170563918156792236420560984332141068171584889135398787064242112798454893526871054391873738069370438288696992737085458297381113704543475266622896061695553001240853415620423619573736895840577821397402299006761384938176594008697709207947638332920539057853169179152921440822903844051469784385505794458097881037425102544892149517586580253692449941230859882387602089377269467779502386280324166006298767114234484854361856079533206880343807190279219812642869539920706440270109515041873398363358197754605023819567931011267739602371024435979931404091419211424992603673642581098633949477686564997804263866336184187364542227619087030827394139885994662292076758735231281117842780351651310925501236221060908052700137797111510660283487755451200613694352294899406873302628027475422270014397358446048817606900849697383707823182402981507022340920306822470255650391866326301830644817599489082157590236725678748053638961685485350332633950712981154963382780116945338832041318133445168670211550375004555148800498070778674121257752245611152733676045229076116999691793999803588160195473015916153144411496392630973653019337919158616148882645161011385092588417754395023739273782663505136046081429384075940970212723904865022448390936149475586564194862780388710148624468591708579182692040441074286293109465012442504757428289604934260710158506825311433207312696913678231700500356073665557578007309238088826328080654854368032552483034772925060236052443196522398670328903361051285107844305940469918414968805723366894228518381492322335299716438126873401451594672668551314446090817622959679366936228534440321991887820427696045883782249681448407612626440121874164246003976413285099197243810710868801214541640854156797177598920846646206070608203467842502410368568670335079834001113000425558986243141798848334853775091149299557085124767841822998344087602151141998966058428198810781898240137562405538566823569667835461231205764872792451361819638342802895777577797309157794677980318051298078437500579044339046364929492473041239692238705855975768461323235211825228050822490020363831315582561840391291914317496650807542955825247815535929469620091325329036155219706407534802880954042717722215599670670462315176767567587599371729171543506766634940183947717391774296854878209218138818700136561816920694704971504842045969017576389073325233918471792356861783505976046402605977466991384437882285072638410126450930701826444815993606115202338165599886847015559153007911444201434547607327026330921832411288863139859435828607816820635843184292982229669676050170254476862005859002240206738902576639220479701948121333105215599053023167332387509442283022049390783590593725815248105830158111531042644222187496718748745403932066209319432975077314000149470645385835000466323707712005889884604955878365482904449345818867518978757256583656929045296399672152815823135461787088330357302783674593757932907444935199534046880664983783670270226868027920128322402005624296268113278984489023481097213360699226149704116063338494805895072842233733795251157007795326509977783226799469070385232794353715488185333717921715675950111392689650146042702898680520083728267307866911831466288501816191870896891813517458109616336029775540796530304555704683063555289006434031871835715701891297781966798987305495146218732377750615022293979112403778272032868718449804113160396208386785559653302220380260733629104034657425016074270851927090442711051624813856546474561887332486333009480268330690832322965299957320571916689262263541453707026417392453708879359277402076653735191134043668899049873166127975284225843968705046857812033869307067676231758559201802047747841785939506388634795654480691419087895533607115790956037718485010008974415196099927920560675508493576776955826483110125895048136341934483680831995612233616442265110277836282702108091982505758016907477052858873151922087499621691031823041579398250946390067737378840762497938602152994940851006795973186695630207152726264277689282645902188139071935527504760516526079848207000785029711923125147077262117776692091088152474881828631287417845189176101743803607924908912465172413154157970707459388146236644149305115910779612945146126085283503196633575183425805427513839931762326850301442762316350297428054898962167250240419209572050718725274806722720217510671401139065141407259949834686701497856455062762229879676130464402824624609415291835258642893010517915786261918276615811647222100408450156172118536398263916983262375953261393894062371259141952024864009506827164375092261064688054145432467371237524296700466385472441504168810417486336097716743244637122949488186569012511681254466362001844294822818608724762159467884502426427398339887600545259032010806357073018880860160328884831632435624166562181332598744817167135975669637756037965543928002090118446221758849496030689658793104832657730133837992349820604343172248859977505285516726815219076407293920435910754907053346814514958491013540681647907688905881052248637624479091712593890109428571252100772862060211964198692193617603442024845480087977680697348501927368383993793879980012933534356939607065143877849129765843733999074764352115781691328293743171137094846536264852101266979896198195605192437279461312735207810520633434359842549351562987362318697357148989498143043407634244095446271788280389636619566942775595767139558023948656215662670694550559681096348654486250244742740636930243532151938763976586226341792424802985954082864796389480972448607112702719562804538719382451528584407988155995471410033186189159425266839072614939529241584710017683242055357256460127470048738548047091900358667784196505722193364368051081901884256602803995189762866674037257720127951813628634622713238096238095620448325465536207410902833580495192542279501459809381691822411579157368501346779926709971977342226630851358854931326885507338576335338010570415806335455363556462536294499171426153780588210224903909522083052561167155740383077205294225553674476404946860714976155726177189420690072616792471126533077792059155787324271623986209171197624281444578199397546828473787357624577915279791136390728619984472347004132678050729842926116412926863766153792941156124559694684589144107613923499441338021688067116025662009811944928096590154578588515342667631019976566461628352975546725944336390481561066479231300882556219800907570935247710535889322545917444027258010422180455539585941606389437737137958317454650791484126155695294824671550609710527242260416158394413503746339667718108245159034913748643492128394049091842299822055814315458414734099751273434310430765752939846712294331171361918461910000
Path 1⅄Zn=(pn2/φn1)
1⅄Zn1=(pn2/φn1)=(3/0)=0
1⅄Zn2=(pn3/φn2)=(5/1)=5
1⅄Zn3=(pn4/φn3)=(7/2)=3.5
1⅄Zn4=(pn5/φn4)=(11/1.5)=7.3
1⅄Zn5=(pn6/φn5)=(13/1.6)=8.125 and then 1⅄Zn5=(pn6/φn5c2)=(13/1.66) and then 1⅄Zn5=(pn6/φn5c3)=(13/1.666) and so on for variable cn of φn5ccn
1⅄Zn6=(pn7/φn6)=(17/1.6)=10.625
1⅄Zn7=(pn8/φn7)=(19/1.625)=11.692307 or 11.692307 and 11.692307692307 and so on for cn of 1⅄Zn7cn
1⅄Zn8=(pn9/φn8)=(23/1.615384)
Path 2⅄Zn=(pn1/φn2)
2⅄Zn1=(pn1/φn2)=(2/1)=2
2⅄Zn2=(pn2/φn3)=(3/2)=1.5
2⅄Zn3=(pn3/φn4)=(5/1.5)3.3 or 3.33 or 3.333
2⅄Zn4=(pn4/φn5)=(7/1.6)=4.375
2⅄Zn5=(pn5/φn6)=(11/1.6)=6.875
2⅄Zn6=(pn6/φn7)=(13/1.625)=8
2⅄Zn7=(pn7/φn8)=(17/1.615384)
2⅄Zn8=(pn8/φn9)=(19/1.619047)
2⅄Zn9=(pn9/φn10)=(23/1.61762941)
Ψ represents unique whole numbers that are not prime numbers nor are they fibonacci numbers
4 6 9 10 12 14 15 16 18 20 22 24 25 26 27 28 30 32 33 35 36 38 39 40 42 44 45 46 48 49 50 51 52 54 56 57 58 60 62 63 64 65 66 68 69 70 72 74 75 76 77 78 80 81 82 84 85 86 87 88 90 91 92 93 94 95 96 98 99 100 and so on . . .
These whole numbers are variables that are neither Y base fibonacci numerals nor are they prime numbers and yet these numbers are still factorable numerals of a set entirely different than Y, P, A through Z, φ, and Θ.
In this case we note the set as (N) of Ψ such that psi represents N whole numbers that are not prime nor fibonacci based numerals and are an ordinal set of consecutive values.
N then is a number and N represents any number of any set including numbers that can not be defined to any of these sets.
A B D E F G H I J K L M O P Q R S T U V W X Y Z φ Θ ᐱ ᗑ ∘⧊° ∘∇° ∀
As C cycles of repeating ratios are numerable then cn or CN is a cycle count of N many cycle counts that its self can be whole and partial of...
1⅄Ψn1=(Ψn2/Ψn1)=(6/4)=1.5
2⅄Ψn1=(Ψn1/Ψn2)=(4/6)=0.6
And path 3⅄ is applicable to variables of 1⅄Ψn and also applicable to variables of 2⅄Ψn to variable factor potential notated change of CN variants in ratios of 1⅄Ψn and 2⅄Ψn
Chevron ^ Bold numerals represent a repeating decimal number sequence stem that can be counted for cn as practical application ratio values infinitely to the limit of a finite factoring limit.
1⅄Ψn1=(Ψn2/Ψn1)=(6/4)=1.5
1⅄Ψn2=(Ψn3/Ψn2)=(9/6)=1.5
1⅄Ψn3=(Ψn4/Ψn3)=(10/9)=1.^1 or 1.1
1⅄Ψn4=(Ψn5/Ψn4)=(12/10)=1.2
1⅄Ψn5=(Ψn6/Ψn5)=(14/12)=1.1^6 or 1.16
1⅄Ψn6=(Ψn7/Ψn6)=(15/14)=1.0^714285 or 1.0714285
1⅄Ψn7=(Ψn8/Ψn7)=(16/15)=1.0^6 or 1.06
1⅄Ψn8=(Ψn9/Ψn8)=(18/16)=1.125
1⅄Ψn9=(Ψn10/Ψn9)=(20/18)=1.^1 or 1.1
1⅄Ψn10=(Ψn11/Ψn10)=(22/20)=1.1
1⅄Ψn11=(Ψn12/Ψn11)=(24/22)=1.^09 or 1.09
1⅄Ψn12=(Ψn13/Ψn12)=(25/24)=1.041^6 or 1.0416
1⅄Ψn13=(Ψn14/Ψn13)=(26/25)=1.04
1⅄Ψn14=(Ψn15/Ψn14)=(27/26)=1.0^384615 or 1.0384615
1⅄Ψn15=(Ψn16/Ψn15)=(28/27)=1.0^37 or 1.037
1⅄Ψn16=(Ψn17/Ψn16)=(30/28)=1.0^714285 or 1.0714285
1⅄Ψn17=(Ψn18/Ψn17)=(32/30)=1.0^6 or 1.06
1⅄Ψn18=(Ψn19/Ψn18)=(33/32)=1.03125
1⅄Ψn19=(Ψn20/Ψn19)=(35/33)=1.0^6 or 1.06
1⅄Ψn20=(Ψn21/Ψn20)=(36/35)=1.0^285714 or 1.0285714
1⅄Ψn21=(Ψn22/Ψn21)=(38/36)=1.0^5 or 1.05
1⅄Ψn22=(Ψn23/Ψn22)=(39/38)=1.0^263157894736842105263157894736842105 or 1.0263157894736842105263157894736842105
1⅄Ψn23=(Ψn24/Ψn23)=(40/39)=^1.02564 or 1.02564 or 1.02564102564
1⅄Ψn24=(Ψn25/Ψn24)=(42/40)=1.05
1⅄Ψn25=(Ψn26/Ψn25)=(44/42)=1.^047619 or 1.047619
1⅄Ψn26=(Ψn27/Ψn26)=(45/44)=1.02^27 or 1.0227
1⅄Ψn27=(Ψn28/Ψn27)=(46/45)=1.0^2 or 1.02
1⅄Ψn28=(Ψn29/Ψn28)=(48/46)=1.^0434782608695652173913 or 1.0434782608695652173913
1⅄Ψn29=(Ψn30/Ψn29)=(49/48)=1.0208^3 or 1.02083
1⅄Ψn30=(Ψn31/Ψn30)=(50/49)=^1.02040816326530612244897959183673469387755 or ^1.02040816326530612244897959183673469387755102040816326530612244897959183673469387755
1⅄Ψn31=(Ψn32/Ψn31)=(51/50)=1.02
1⅄Ψn32=(Ψn33/Ψn32)=(52/51)=1.^0196078431372549 or 1.0196078431372549
1⅄Ψn33=(Ψn34/Ψn33)=(54/52)=1.0^384615 or 1.0384615
1⅄Ψn34=(Ψn35/Ψn34)=(56/54)=1.^037 or 1.037
1⅄Ψn35=(Ψn36/Ψn35)=(57/56)=1.017^857142 or 1.017857142
1⅄Ψn36=(Ψn37/Ψn36)=(58/57)=1.^017543859649122807 or 1.017543859649122807
1⅄Ψn37=(Ψn38/Ψn37)=(60/58)=^1.034482758620689655172413793 or 1.034482758620689655172413793
1⅄Ψn38=(Ψn39/Ψn38)=(62/60)=1.0^3 or 1.03 or 1.033 or 1.0333
1⅄Ψn39=(Ψn40/Ψn39)=(63/62)=1.0^161290322580645 or 1.0161290322580645
1⅄Ψn40=(Ψn41/Ψn40)=(64/63)=1.^015873 or 1.015873
1⅄Ψn41=(Ψn42/Ψn41)=(65/64)=1.015625
1⅄Ψn42=(Ψn43/Ψn42)=(66/65)=1.0^153846 or 1.0153846
1⅄Ψn43=(Ψn44/Ψn43)=(68/66)=1.^03 or 1.03
1⅄Ψn44=(Ψn45/Ψn44)=(69/68)=1.01^4705882352941176 or 1.014705882352941176
1⅄Ψn45=(Ψn46/Ψn45)=(70/69)=^1.014492753623188405797 or 1.0144927536231884057971014492753623188405797
1⅄Ψn46=(Ψn47/Ψn46)=(72/70)=1.0^285714 or 1.0285714
1⅄Ψn47=(Ψn48/Ψn47)=(74/72)=1.02^7 or 1.027
1⅄Ψn48=(Ψn49/Ψn48)=(75/74)=1.0^135 or 1.0135
1⅄Ψn49=(Ψn50/Ψn49)=(76/75)=1.01^3 or 1.013
1⅄Ψn50=(Ψn51/Ψn50)=(77/76)=1.01^315789473684210526 or 1.01315789473684210526
1⅄Ψn51=(Ψn52/Ψn51)=(78/77)=1.^012987 or 1.012987
1⅄Ψn51=(Ψn53/Ψn52)=(80/78)=^1.02564 or 1.02564102564
1⅄Ψn53=(Ψn54/Ψn53)=(81/80)=1.0125
1⅄Ψn54=(Ψn55/Ψn54)=(82/81)=1.^012345679 or 1.012345679
1⅄Ψn55=(Ψn56/Ψn55)=(84/82)=1.^02439 or 1.02439
1⅄Ψn56=(Ψn57/Ψn56)=(85/84)=1.01^190476 or 1.01190476
1⅄Ψn57=(Ψn58/Ψn57)=(86/85)=1.0^1176470588235294 or 1.0^1176470588235294
1⅄Ψn58=(Ψn59/Ψn58)=(87/86)=1.0^116279069767441860465 or 1.0116279069767441860465
1⅄Ψn59=(Ψn60/Ψn59)=(88/87)=1.^0114942528735632183908045977 or 1.0114942528735632183908045977
1⅄Ψn60=(Ψn61/Ψn60)=(90/88)=1.02^27 or 1.0227
1⅄Ψn61=(Ψn62/Ψn61)=(91/90)=1.0^1 or 1.01 or 1.011 or 1.0111
1⅄Ψn62=(Ψn63/Ψn62)=(92/91)=1.^010989 or 1.010989
1⅄Ψn63=(Ψn64/Ψn63)=(93/92)=1.01^0869565217391304347826 or 1.010869565217391304347826
1⅄Ψn64=(Ψn65/Ψn64)=(94/93)=1.^010752688172043 or 1.010752688172043
1⅄Ψn65=(Ψn66/Ψn65)=(95/94)=1.0^1063829787234042553191489361702127659574468085 or 1.01063829787234042553191489361702127659574468085
1⅄Ψn66=(Ψn67/Ψn66)=(96/95)=1.0^105263157894736842 or 1.0105263157894736842
1⅄Ψn67=(Ψn68/Ψn67)=(98/96)=1.0208^3 or 1.02083
1⅄Ψn68=(Ψn69/Ψn68)=(99/98)=1.0^102040816326530612244897959183673469387755 or 1.0102040816326530612244897959183673469387755
1⅄Ψn69=(Ψn70/Ψn69)=(100/99)=1.^01 or 1.01 or 1.0101 or 1.010101
and so on for variables of 1⅄Ψn
Then
2⅄Ψn1=(Ψn1/Ψn2)=(4/6)=0.^6 or 0.6
2⅄Ψn2=(Ψn2/Ψn3)=(6/9)=0.^6 or 0.6
2⅄Ψn3=(Ψn3/Ψn4)=(9/10)=0.9
2⅄Ψn4=(Ψn4/Ψn5)=(10/12)=0.8^3 or 0.83
2⅄Ψn5=(Ψn5/Ψn6)=(12/14)=0.^857142 or 0.857142
2⅄Ψn6=(Ψn6/Ψn7)=(14/15)=0.9^3 or 0.93
2⅄Ψn7=(Ψn7/Ψn8)=(15/16)=0.9375
2⅄Ψn8=(Ψn8/Ψn9)=(16/18)=0.^8 or 0.8
2⅄Ψn9=(Ψn9/Ψn10)=(18/20)=0.9
2⅄Ψn10=(Ψn10/Ψn11)=(20/22)=0.9^09 or 0.909
2⅄Ψn11=(Ψn11/Ψn12)=(22/24)=0.91^6 or 0.916
2⅄Ψn12=(Ψn12/Ψn13)=(24/25)=0.96
2⅄Ψn13=(Ψn13/Ψn14)=(25/26)=0.9^615384 or 0.9615384
2⅄Ψn14=(Ψn14/Ψn15)=(26/27)=0.^962 or 0.962
2⅄Ψn15=(Ψn15/Ψn16)=(27/28)=0.96^428571 or 0.96428571
2⅄Ψn16=(Ψn16/Ψn17)=(28/30)=0.9^3 or 0.93
2⅄Ψn17=(Ψn17/Ψn18)=(30/32)=0.9375
2⅄Ψn18=(Ψn18/Ψn19)=(32/33)=0.^96 or 0.96
2⅄Ψn19=(Ψn19/Ψn20)=(33/35)=0.9^428571 or 0.9428571
2⅄Ψn20=(Ψn20/Ψn21)=(35/36)=0.97^2 or 0.972
and so on for variables of 2⅄Ψn
⅄ᐱ∀Ψ complex for all for any equations of psi specific numerals can then be factored to a library of psi Ψ and many paths the variables can be quantified with.
Then
1⅄2Ψn1 of 1⅄Ψn=(1⅄Ψn2/1⅄Ψn1)=(1.5/1.5)=1
1⅄2Ψn2 of 1⅄Ψn=(1⅄Ψn3/1⅄Ψn2)=(1.1/1.5)=0.73 or 0.733 and 1⅄2Ψn2 of 1⅄Ψn=(1⅄Ψn3c2/1⅄Ψn2)=(1.11/1.5)=0.74 and 1⅄2Ψn2 of 1⅄Ψn=(1⅄Ψn3c3/1⅄Ψn2)=(1.111/1.5)=0.7406 or 0.740666 and so on for cn variable of 1⅄2Ψn2 of 1⅄Ψn
1⅄2Ψn3 of 1⅄Ψn=(1⅄Ψn4/1⅄Ψn3)=(1.2/1.1)=1.09 or 1.090909
1⅄2Ψn4 of 1⅄Ψn=(1⅄Ψn5/1⅄Ψn4)=(1.16/1.2)=0.96 or 0.9666
1⅄2Ψn5 of 1⅄Ψn=(1⅄Ψn6/1⅄Ψn5)=(1.0714285/1.16)=0.923645258620689655172413793103448275862068965517241379310344827
or
0.92364525862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827
1⅄2Ψn6 of 1⅄Ψn=(1⅄Ψn7/1⅄Ψn6)=(1.06/1.0714285)
1⅄2Ψn7 of 1⅄Ψn=(1⅄Ψn8/1⅄Ψn7)=(1.125/1.06)
1⅄2Ψn8 of 1⅄Ψn=(1⅄Ψn9/1⅄Ψn8)=(1.1/1.125)
1⅄2Ψn9 of 1⅄Ψn=(1⅄Ψn10/1⅄Ψn9)=(1.1/1.1)
1⅄2Ψn10 of 1⅄Ψn=(1⅄Ψn11/1⅄Ψn10)=(1.09/1.1)
1⅄2Ψn11 of 1⅄Ψn=(1⅄Ψn12/1⅄Ψn11)=(1.0416/1.09)
1⅄2Ψn12 of 1⅄Ψn=(1⅄Ψn13/1⅄Ψn12)=(1.04/1.0416)
1⅄2Ψn13 of 1⅄Ψn=(1⅄Ψn14/1⅄Ψn13)=(1.0384615/1.04)
1⅄2Ψn14 of 1⅄Ψn=(1⅄Ψn15/1⅄Ψn14)=(1.037/1.0384615)
1⅄2Ψn15 of 1⅄Ψn=(1⅄Ψn16/1⅄Ψn15)=(1.0714285/1.037)
1⅄2Ψn16 of 1⅄Ψn=(1⅄Ψn17/1⅄Ψn16)=(1.06/1.0714285)
1⅄2Ψn17 of 1⅄Ψn=(1⅄Ψn18/1⅄Ψn17)=(1.03125/1.06)
1⅄2Ψn18 of 1⅄Ψn=(1⅄Ψn19/1⅄Ψn18)=(1.06/1.03125)
1⅄2Ψn19 of 1⅄Ψn=(1⅄Ψn20/1⅄Ψn19)=(1.0285714/1.06)
and so on for c1 of cn variables factoring for 1⅄2Ψn of 1⅄Ψn from Ψ base numerals.
Then
2⅄2Ψn1 of 1⅄Ψn=(1⅄Ψn1/1⅄Ψn2)=(1.5/1.5)=1
2⅄2Ψn2 of 1⅄Ψn=(1⅄Ψn2/1⅄Ψn3)=(1.5/1.1)=1.^36 or 1.36
2⅄2Ψn3 of 1⅄Ψn=(1⅄Ψn3/1⅄Ψn4)=(1.1/1.2)=0.916 or 0.91666
2⅄2Ψn4 of 1⅄Ψn=(1⅄Ψn4/1⅄Ψn5)=(1.2/1.16)=1.034482758620689655172413793 or 1.0344827586206896551724137931034482758620689655172413793
2⅄2Ψn5 of 1⅄Ψn=(1⅄Ψn5/1⅄Ψn6)=(1.16/1.0714285)
2⅄2Ψn6 of 1⅄Ψn=(1⅄Ψn6/1⅄Ψn7)=(1.0714285/1.06)
2⅄2Ψn7 of 1⅄Ψn=(1⅄Ψn7/1⅄Ψn8)=(1.06/1.125)
2⅄2Ψn8 of 1⅄Ψn=(1⅄Ψn8/1⅄Ψn9)=(1.125/1.1)
2⅄2Ψn9 of 1⅄Ψn=(1⅄Ψn9/1⅄Ψn10)=(1.1/1.1)
2⅄2Ψn10 of 1⅄Ψn=(1⅄Ψn10/1⅄Ψn11)=(1.1/1.09)
2⅄2Ψn11 of 1⅄Ψn=(1⅄Ψn11/1⅄Ψn12)=(1.09/1.0416)
2⅄2Ψn12 of 1⅄Ψn=(1⅄Ψn12/1⅄Ψn13)=(1.0416/1.04)
2⅄2Ψn13 of 1⅄Ψn=(1⅄Ψn13/1⅄Ψn14)=(1.04/1.0384615)
2⅄2Ψn14 of 1⅄Ψn=(1⅄Ψn14/1⅄Ψn15)=(1.0384615/1.037)
2⅄2Ψn15 of 1⅄Ψn=(1⅄Ψn15/1⅄Ψn16)=(1.037/1.0714285)
2⅄2Ψn16 of 1⅄Ψn=(1⅄Ψn16/1⅄Ψn17)=(1.0714285/1.06)
2⅄2Ψn17 of 1⅄Ψn=(1⅄Ψn17/1⅄Ψn18)=(1.06/1.03125)
2⅄2Ψn18 of 1⅄Ψn=(1⅄Ψn18/1⅄Ψn19)=(1.03125/1.06)
2⅄2Ψn19 of 1⅄Ψn=(1⅄Ψn19/1⅄Ψn20)=(1.06/1.0285714)
and so on for c1 of cn variables factoring for 2⅄2Ψn of 1⅄Ψn from Ψ base numerals.
Then
1⅄2Ψn1 of 2⅄Ψn=(2⅄Ψn2/2⅄Ψn1)=(0.6/0.6)=1
1⅄2Ψn2 of 2⅄Ψn=(2⅄Ψn3/2⅄Ψn2)=(0.9/0.6)=1.5
1⅄2Ψn3 of 2⅄Ψn=(2⅄Ψn4/2⅄Ψn3)=(0.83/0.9)=0.92 or 0.9222
1⅄2Ψn4 of 2⅄Ψn=(2⅄Ψn5/2⅄Ψn4)=(0.857142/0.83)=1.032701204819277108433734939759036144578313253 or 1.032701204819277108433734939759036144578313253
1⅄2Ψn5 of 2⅄Ψn=(2⅄Ψn6/2⅄Ψn5)=(0.93/0.857142)=1.08500 or 1.08500108500
1⅄2Ψn6 of 2⅄Ψn=(2⅄Ψn7/2⅄Ψn6)=(0.9375/0.93)=1.00806451612903225 or 1.00806451612903225
1⅄2Ψn7 of 2⅄Ψn=(2⅄Ψn8/2⅄Ψn7)=(0.8/0.9375)
1⅄2Ψn8 of 2⅄Ψn=(2⅄Ψn9/2⅄Ψn8)=(0.9/0.8)
1⅄2Ψn9 of 2⅄Ψn=(2⅄Ψn10/2⅄Ψn9)=(0.909/0.9)
1⅄2Ψn10 of 2⅄Ψn=(2⅄Ψn11/2⅄Ψn10)=(0.916/0.909)
1⅄2Ψn11 of 2⅄Ψn=(2⅄Ψn12/2⅄Ψn11)=(0.96/0.916)
1⅄2Ψn12 of 2⅄Ψn=(2⅄Ψn13/2⅄Ψn12)=(0.9615384/0.96)
1⅄2Ψn13 of 2⅄Ψn=(2⅄Ψn14/2⅄Ψn13)=(0.962/0.9615384)
1⅄2Ψn14 of 2⅄Ψn=(2⅄Ψn15/2⅄Ψn14)=(0.96428571/0.962)
1⅄2Ψn15 of 2⅄Ψn=(2⅄Ψn16/2⅄Ψn15)=(0.93/0.96428571)
1⅄2Ψn16 of 2⅄Ψn=(2⅄Ψn17/2⅄Ψn16)=(0.9375/0.93)
1⅄2Ψn17 of 2⅄Ψn=(2⅄Ψn18/2⅄Ψn17)=(0.96/0.9375)
1⅄2Ψn18 of 2⅄Ψn=(2⅄Ψn19/2⅄Ψn18)=(0.9428571/0.96)
1⅄2Ψn19 of 2⅄Ψn=(2⅄Ψn20/2⅄Ψn19)=(0.972/0.9428571)
and so on for c1 of cn variables factoring for 1⅄2Ψn of 2⅄Ψn from Ψ base numerals.
while
2⅄2Ψn1 of 2⅄Ψn=(2⅄Ψn1/2⅄Ψn2)=(0.6/0.6)=1
2⅄2Ψn2 of 2⅄Ψn=(2⅄Ψn2/2⅄Ψn3)=(0.6/0.9)=0.6 or 0.6
2⅄2Ψn3 of 2⅄Ψn=(2⅄Ψn3/2⅄Ψn4)=(0.9/0.83)=1.0843373493975903614457831325301204819277 or 1.084337349397590361445783132530120481927710843373493975903614457831325301204819277
2⅄2Ψn4 of 2⅄Ψn=(2⅄Ψn4/2⅄Ψn5)=(0.83/0.857142)=0.96833430166763500 or 0.96833430166763500096833430166763500
2⅄2Ψn5 of 2⅄Ψn=(2⅄Ψn5/2⅄Ψn6)=(0.857142/0.93)=0.92165806451612903225 or 0.92165806451612903225
2⅄2Ψn6 of 2⅄Ψn=(2⅄Ψn6/2⅄Ψn7)=(0.93/0.9375)=0.992
2⅄2Ψn7 of 2⅄Ψn=(2⅄Ψn7/2⅄Ψn8)=(0.9375/0.8)
2⅄2Ψn8 of 2⅄Ψn=(2⅄Ψn8/2⅄Ψn9)=(0.8/0.9)
2⅄2Ψn9 of 2⅄Ψn=(2⅄Ψn9/2⅄Ψn10)=(0.9/0.909)
2⅄2Ψn10 of 2⅄Ψn=(2⅄Ψn10/2⅄Ψn11)=(0.909/0.916)
2⅄2Ψn11 of 2⅄Ψn=(2⅄Ψn11/2⅄Ψn12)=(0.916/0.96)
2⅄2Ψn12 of 2⅄Ψn=(2⅄Ψn12/2⅄Ψn13)=(0.96/0.9615384)
2⅄2Ψn13 of 2⅄Ψn=(2⅄Ψn13/2⅄Ψn14)=(0.9615384/0.962)
2⅄2Ψn14 of 2⅄Ψn=(2⅄Ψn14/2⅄Ψn15)=(0.962/0.96428571)
2⅄2Ψn15 of 2⅄Ψn=(2⅄Ψn15/2⅄Ψn16)=(0.96428571/0.93)
2⅄2Ψn16 of 2⅄Ψn=(2⅄Ψn16/2⅄Ψn17)=(0.93/0.9375)
2⅄2Ψn17 of 2⅄Ψn=(2⅄Ψn17/2⅄Ψn18)=(0.9375/0.96)
2⅄2Ψn18 of 2⅄Ψn=(2⅄Ψn18/2⅄Ψn19)=(0.96/0.9428571)
2⅄2Ψn19 of 2⅄Ψn=(2⅄Ψn19/2⅄Ψn20)=(0.9428571/0.972)
and so on for c1 of cn variables factoring for 2⅄2Ψn of 2⅄Ψn from Ψ base numerals.