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1 decimal integer ring cycle of many

Quantum Field Fractal Polarization Math Constants

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pronounced why phi prime quotients

ᐱ Y φ Θ P Q Ψ

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numer nu mer numerical nomenclature & arcs

T=∈(Θ/P)cn

T represents ∈(Θ/P)cn

3⅄Θncn/pn that path 3⅄ of Θncn/pn  differ from paths 2⅄Θncn/pn and 1⅄Θncn/pn

Path 1⅄T=Θn2cn/pn1

1⅄Tn1=1Θn2/pn1=(Θn2/pn1)=(1/2)=0.5

1⅄Tn2=1Θn3/pn2=(0.5/3)=0.1^6

1⅄Tn3=1Θn4/pn3=(0.^6/5)=0.12

1⅄Tn4=1Θn5/pn4=(0.6/7)=0.0^857142 or 0.0857142

1⅄Tn5=1Θn6/pn5=(0.625/11)=0.056^81 or 0.05681

1⅄Tn6=1Θn7/pn6=(0.^615384/13)=0.047337^230769 or 0.047337230769

1⅄Tn7=1Θn8/pn7=(0.^619047/17)=0.036414^5294117647058823 or 0.0364145294117647058823

1⅄Tn8=1Θn9/pn8=(0.6^1764705882352941/19)=0.03250773993808049^526315789473684210526315789473684210526315789473684210526315789473684210

or

0.03250773993808049526315789473684210526315789473684210526315789473684210526315789473684210

1⅄Tn9=1Θn10/pn9=(0.6^18/23)

1⅄Tn10=1Θn11/pn10=(0.^6179775280878651685393258764044943820224719101123595505/29)

1⅄Tn11=1Θn12/pn11=(0.6180^5/31)=0.01993^709677419354838 or 0.01993709677419354838

1⅄Tn12=1Θn13/pn12=(0.6180257553648064377682403433476394849785407725322060085836909871244635193133047210300429184^54935622317596566/37)=0.016703398793643417236979468739125391485906507365735297529288945597958473494954181649460619417700962765340447^729

or

0.016703398793643417236979468739125391485906507365735297529288945597958473494954181649460619417700962765340447729

1⅄Tn13=1Θn14/pn13=(0.610079575596814323607427055702917771827585941644562334217506631^294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/41)=0.014879989648702788380668952578119945654331364430355178883353820275473895321860639192534062237174095878889816911431066830562204826227599146011515817428989454616^02439

or

0.01487998964870278838066895257811994565433136443035517888335382027547389532186063919253406223717409587888981691143106683056220482622759914601151581742898945461602439

1⅄Tn14=1Θn15/pn14=(0.6^18032786885245901639344262295081967213114754098360655737749/47)=0.0131496337635158702476456226020230205790024415765608650156967872340425531914893617021276595744^6808510638297872340425531914893617021276595744

or

0.01314963376351587024764562260202302057900244157656086501569678723404255319148936170212765957446808510638297872340425531914893617021276595744

1⅄Tn15=1Θn16/pn15=(0.^618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870/53)=0.01166102731739022385349161744183823669973810479631435071017568006728986255280916059719753015618130030012808013610904016363671101928848616^7358490566037

or

0.011661027317390223853491617441838236699738104796314350710175680067289862552809160597197530156181300300128080136109040163636711019288486167358490566037

1⅄Tn16=1Θn17/pn16=(0.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/59)=0.0104751493796631395731403160587117795018201500695159355995882109463719049488978274943485136325525614764972458953758636426350254184222^5254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491

or

0.0104751493796631395731403160587117795018201500695159355995882109463719049488978274943485136325525614764972458953758636426350254184222^5254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491

1⅄Tn17=1Θn18/pn17=(0.618^034055727554179566563467492260061919504643962848297213622291021671826625386996904024767801857585139318885448916408668730650154798761609907120743/61)=0.010131705831599248845353499467086230523270567933817185200223316246256915190580114703344668324620616149824899761457646043749682789422930518195198700^704918032786885245901639344262295081967213114754098360655737

or

0.010131705831599248845353499467086230523270567933817185200223316246256915190580114703344668324620616149824899761457646043749682789422930518195198700704918032786885245901639344262295081967213114754098360655737

1⅄Tn18=1Θn19/pn18=(0.^618033963166706529538387945467591485290600334848122458741927768476441042812724228653432193255202104759626883520688830423343697679980865821573786175556087060511839272901219803874671131308299449892370246352547237502989715379095910069361396795025113609184405644582635733078210954317149007414494140157856972016264051662281750777325998564936/67)=0.009224387509950843724453551424889425153591049773852574011073548783230463325563048188857196914256747832233237067472967618258861159402699489874235614560538612843460287655242086624995091512064170893915973826157421455268503214613371792080020847686941994166931427531084115419077775437569388170365584181460551821138269427795250011601880575596^059701492537313432835820895522388

or

0.009224387509950843724453551424889425153591049773852574011073548783230463325563048188857196914256747832233237067472967618258861159402699489874235614560538612843460287655242086624995091512064170893915973826157421455268503214613371792080020847686941994166931427531084115419077775437569388170365584181460551821138269427795250011601880575596059701492537313432835820895522388

1⅄Tn19=1Θn20/pn19=(0.6^1803399852/71)=0.00870470420^4507042253521126760563380281690140845070422535211267605633802816901408450704225352112676056338028169014084507042253521126760563380281690140845070422535211267605633802816901408

or

0.008704704204507042253521126760563380281690140845070422535211267605633802816901408450704225352112676056338028169014084507042253521126760563380281690140845070422535211267605633802816901408

1⅄Tn20=1Θn21/pn20=(0.6^180339850173579389731408733784030696144710396491869175954686643522748035812168828795907180705280467750776539375114196966928558377489493879042572629270966563128083318107071076192216334734149460990316097204458249588890919057189841037822035446738534624520372738900054814544125708021194957061940434862050063950301479992691394116572263840672391741275351726658139959802667641147451123698154577014434496619769778914672026310981/73)=0.0084662189728405197119608338818959324604722060225916016108968310185243123778248888065697358639798362571928445744864578040642856964075198546288254419579054336481206620795987275016331730612796567958771453386362441775190286562427258096408521033516966227733155790943836367322522269972893081603588225135096576218497280547845087590637976216995512215633908927762440273421954351248595220872577459959101842419448901081022904470013^43835616

or

0.0084662189728405197119608338818959324604722060225916016108968310185243123778248888065697358639798362571928445744864578040642856964075198546288254419579054336481206620795987275016331730612796567958771453386362441775190286562427258096408521033516966227733155790943836367322522269972893081603588225135096576218497280547845087590637976216995512215633908927762440273421954351248595220872577459959101842419448901081022904470013^43835616

1⅄Tn21=1Θn22/pn21=(0.^618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793348766303427248602563378691208853255039241149568065044322737281915193947264411947377336118796228332674609000056462085709446106939190333690926542826492010614872113375868104567782733894190051380497995595957314663203658743153972107729659533623172039975156682287843712946756253175992321156343515329456270114/79)=0.007823215065513887171599713830137746047832677825194812063446231298720883610200054460897861516371503370929458843070422515078593079177711913285671709421806801036901189205878632245282735680964915603476063291853950452018305151128991565707930921854329248289520422479343095794718150559367738993645513872877400800046313204480659591514677640799646075634894712504350796794382951594839508308145763664003419^1645569620253

or

0.0078232150655138871715997138301377460478326778251948120634462312987208836102000544608978615163715033709294588430704225150785930791777119132856717094218068010369011892058786322452827356809649156034760632918539504520183051511289915657079309218543292482895204224793430957947181505593677389936455138728774008000463132044806595915146776407996460756348947125043507967943829515948395083081457636640034191645569620253

and so on for cn of variable Θncn and beyond variable 1⅄Tn21

Path 2⅄T=Θn1cn/pn1

2⅄Tn1=1Θn1/pn2=(Θn1/pn2)=(0/3)=0

2⅄Tn2=1Θn2/pn3=(1/5)=0.2

2⅄Tn3=1Θn3/pn4=(0.5/7)=0.0^714285 or 0.0714285

2⅄Tn4=1Θn4/pn5=(0.^6/11)=0.0^54 or 0.054 and 2⅄Tn4=1Θn4c2/pn5=(0.^66/11)=0.06 and so on for cn of 2⅄Tn4=1Θn4cn/pn5

2⅄Tn5=1Θn5/pn6=(0.6/13)=0.0^461538 or 0.0461538

2⅄Tn6=1Θn6/pn7=(0.625/17)=0.036^7647058823529411 or 0.0367647058823529411

2⅄Tn7=1Θn7/pn8=(0.^615384/19)=0.032388^631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052

or

0.032388631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052

2⅄Tn8=1Θn8/pn9=(0.^619047/23)=0.026915^0869565217391304347826 or 0.0269150869565217391304347826

2⅄Tn9=1Θn9/pn10=(0.6^1764705882352941/29)=0.02129817444219066^931034482758620689655172413793103448275862068965517241379310344827586206896551724137

or

0.02129817444219066931034482758620689655172413793103448275862068965517241379310344827586206896551724137

2⅄Tn10=1Θn10/pn11=(0.6^18/31)=0.019^935483870967741 or 0.019935483870967741

2⅄Tn11=1Θn11/pn12=(0.^6179775280878651685393258764044943820224719101123595505/37)=0.0167020953537260856361979966595809292438505921651989067^702 or 0.0167020953537260856361979966595809292438505921651989067702

2⅄Tn12=1Θn12/pn13=(0.6180^5/41)=0.01507^43902 or 0.0150743902

2⅄Tn13=1Θn13/pn14=(0.6180257553648064377682403433476394849785407725322060085836909871244635193133047210300429184^54935622317596566/43)=0.014372691985228056692284659147619522906477692384469907176364906677313105100309412116977742289649665635292943^395348837209302325581395348837209302325581

or

0.014372691985228056692284659147619522906477692384469907176364906677313105100309412116977742289649665635292943395348837209302325581395348837209302325581

2⅄Tn14=1Θn14/pn15=(0.610079575596814323607427055702917771827585941644562334217506631^294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/47)=0.012980416502059879225689937355381229187820977481799198600372481516902759748857153338168011738811445341159201986567526384107455273943224786946215925842309949771^4255319148936170212765957446808510638297872340

or

0.0129804165020598792256899373553812291878209774817991986003724815169027597488571533381680117388114453411592019865675263841074552739432247869462159258423099497714255319148936170212765957446808510638297872340

2⅄Tn15=1Θn15/pn16=(0.6^18032786885245901639344262295081967213114754098360655737749/53)=0.011660995978966903804515929477265697494587070832044540674297^1509433962264 or 0.0116609959789669038045159294772656974945870708320445406742971509433962264

2⅄Tn16=1Θn16/pn17=(0.^618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870/59)=0.01047516013257087905483145295622756856078168735940102690914086514519258839489636460426218810640015111706420757989456150292789294953033503^1694915254237288135593220338983050847457627118644067796610

or

0.010475160132570879054831452956227568560781687359401026909140865145192588394896364604262188106400151117064207579894561502927892949530335031694915254237288135593220338983050847457627118644067796610

2⅄Tn17=1Θn17/pn18=(0.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/61)=0.0101317018590184464723816171715409014853670303951055770553394171448515146227044561010911853167311660182514345545438681133683032735559^491803278688524590163934426229508196721311475409836065573770

or

0.0101317018590184464723816171715409014853670303951055770553394171448515146227044561010911853167311660182514345545438681133683032735559491803278688524590163934426229508196721311475409836065573770

2⅄Tn18=1Θn18/pn19=(0.618^034055727554179566563467492260061919504643962848297213622291021671826625386996904024767801857585139318885448916408668730650154798761609907120743/67)=0.009224388891456032530844230858093433759992606626311168615128690910771221292916223834388429370176978882676401275356961323413890300817891964326971951^388059701492537313432835820895522

or

0.009224388891456032530844230858093433759992606626311168615128690910771221292916223834388429370176978882676401275356961323413890300817891964326971951388059701492537313432835820895522

2⅄Tn19=1Θn19/pn20=(0.^618033963166706529538387945467591485290600334848122458741927768476441042812724228653432193255202104759626883520688830423343697679980865821573786175556087060511839272901219803874671131308299449892370246352547237502989715379095910069361396795025113609184405644582635733078210954317149007414494140157856972016264051662281750777325998564936/71)=0.008704703706573331401949125992501288525219723026029893785097574203893535814263721530330030890918339503656716669305476484835826727887054448191180086979663198035378017928186194420770015933919710561864369666937285035253376272945012817878329532324297374777245149923699094832087478229819000104429494931800802422764282417778616208131352092463^88732394366197183098591549295774647

or

0.00870470370657333140194912599250128852521972302602989378509757420389353581426372153033003089091833950365671666930547648483582672788705444819118008697966319803537801792818619442077001593391971056186436966693728503525337627294501281787832953232429737477724514992369909483208747822981900010442949493180080242276428241777861620813135209246388732394366197183098591549295774647

2⅄Tn20=1Θn20/pn21=(0.6^1803399852/73)=0.00846621915^78082191 or 0.0084662191578082191

and so on for cn of variable Θncn and beyond variable 2⅄Tn17=(1Θn17/pn18)

Path 3⅄T=Θn1cn/pn1

3⅄Tn1=1Θn1c1/pn1=(Θn1c1/pn1)=(0/2)

3⅄Tn2=1Θn2c1/pn2=(1/3)=0.^3 or 0.3 or 0.33 and so on for cn of 3⅄Tn2=1Θn2c1/pn2

3⅄Tn3=1Θn3c1/pn3=(0.5/5)=0.1

3⅄Tn4=1Θn4c1/pn4=(0.^6/7)=0.0^857142 or 0.0857142 and 3⅄Tn4=1Θn4c2/pn4=(0.^66/7)=0.09^428571 or 0.09428571

3⅄Tn5=1Θn5c1/pn5=(0.6/11)=0.0^54 or 0.054

3⅄Tn6=1Θn6c1/pn6=(0.625/13)=0.048^076923 or 0.048076923

3⅄Tn7=1Θn7c1/pn7=(0.^615384/17)=0.036199^0588235294117647 or 0.0361990588235294117647

3⅄Tn8=1Θn8c1/pn8=(0.^619047/19)=0.032581^421052631578947368 or 0.032581421052631578947368

3⅄Tn9=1Θn9c1/pn9=(0.6^1764705882352941/23)=0.02685421994884910^4782608695652173913043

or

0.026854219948849104782608695652173913043

3⅄Tn10=1Θn10c1/pn10=(0.6^18/29)=0.021^3103448275862068965517241379 or 0.0213103448275862068965517241379

3⅄Tn11=1Θn11c1/pn11=(0.^6179775280878651685393258764044943820224719101123595505/31)

3⅄Tn12=1Θn12c1/pn12=(0.6180^5/37)

3⅄Tn13=1Θn13c1/pn13=(0.6180257553648064377682403433476394849785407725322060085836909871244635193133047210300429184^54935622317596566/41)

3⅄Tn14=1Θn14c1/pn14=(0.610079575596814323607427055702917771827585941644562334217506631^294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/43)

3⅄Tn15=1Θn15c1/pn15=(0.6^18032786885245901639344262295081967213114754098360655737749/47)

3⅄Tn16=1Θn16c1/pn16=(0.^618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870/53)

3⅄Tn17=1Θn17c1/pn17=(0.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/59)

3⅄Tn18=1Θn18c1/pn18=(0.618^034055727554179566563467492260061919504643962848297213622291021671826625386996904024767801857585139318885448916408668730650154798761609907120743/61)

3⅄Tn19=1Θn19c1/pn19=(0.^618033963166706529538387945467591485290600334848122458741927768476441042812724228653432193255202104759626883520688830423343697679980865821573786175556087060511839272901219803874671131308299449892370246352547237502989715379095910069361396795025113609184405644582635733078210954317149007414494140157856972016264051662281750777325998564936/67)

3⅄Tn20=1Θn20c1/pn20=(0.6^1803399852/71)

and so on for cn of variable Θncn and beyond variable where c1, c2, c3, . . . of theta quotient ratio decimal stem count variable changes the quotient of 3⅄Tn=Θncn/Pn variables and the cn of 3⅄Tncn is then dependent of definition to variable Θncn

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