About

Biblical mathematics has three primary goals (each one corresponding to one of the three persons of the Trinity: Father, Son and Holy Ghost) to prove, using mathematics, the highest form of proof and the very basis of science and the scientific method, that:

1. God Exists

2. Jesus Christ is the Son of God

3. The Bible is the inspired Word of God

Formulas discovered by John Elias:

Omni-Cross Cubes: (2*n+4)^3 - (2*n)^3 Omni-cross cubes are inverted double-hulled cubes which are the product of the 'cubing' of a single -hulled cube:

(3³ - 1³) x 2³ = 6³ - 2³ & (4³ - 2³) x 2³ = 8³ - 4³ & (5³ - 3³) x 2³ = 10³ - 6³ & (6³ - 4³) x 2³ = 12³ - 8³ & (7³ - 5³) x 2³ = 14³ - 10³

Whereas: (8³ - 6³) x 2³ = 16³ - 12³ = 2368 = Jesus Christ

By multiplying Omni-Cross Cubes by EIGHT the formula finds equilibrium the seventh power of two and the difference of all positive cubes:

2^7*(3*n^2+1) numbers which are the third spoke of the hexagonal spiral of numbers (A056107) or half the difference in cubes (A181123)

The next iteration involves triple-hulled cubes which are 72n multiples of Hogben's central polygonals (A002061) 72*(n^2 - n+1):

8³ - 2³ = (4³ - 1³) x 2³ & 10³ - 4³ = (5³ - 2³) x 2³ & 12³ - 6³ = (6³ - 3³) x 2³

The infinite sequence of sequences is as follows:

(3³ - 1³) x 2³ = 6³ - 2³ & (4³ - 1³) x 2³ = 8³ - 2³ & (5³ - 1³) x 2³ = 10³ - 2³ & (6³ - 1³) x 2³ = 12³ - 2³ & Etc. Ad Infinitum

Unilateral Gnomen Cubes: 6*((2*n+1)^2)+2 or 8*(3*(n*(n+1) or 24n+8 Odd numbers squared times six plus two.

Double-hulled Diamonds: (ODD) 2*(2*n+1)^2+3 (EVEN): 8*n^2+3 Nth octahedron minus (N-4th) octahedron (A139098)

Cruciform Fractal (Crossbox): 27*(2*n+1) Three to the third times the odd numbers (A005408) 4/28/2020

Conjecture: Each crossbox iteration has its own iteration and inverse iteration, i.e. an infinitely infinite series of series and an infinitely infinite inverse series of series. The even ordered cubes can crossbox only with a double-bar, starting after 4^3 where 216 becomes 160, 256, 352 with the formula 2^5*(3n+2), n>0.

David Cubes: 27*(2*n+1)+(8*n) Crossboxes with lines from the center to the corners. Alternate from the corner vertices to the midpoint of the twelve edges 2*(11*n+5) - 1 (A017449)

Anti-Cubes: 18*(n*(n+1)*(2*n+1)/6) These are the square pyramids times eighteen. C. Cubes plus Anti C. Cubes equals Odd Cubes. There are no even ordered anti-cubes.

Basketbox Fractal: (2^n+1)^2*((2^n+2)+1) This is a convolution of itself (A000051) 4/28/2020

Antibox Fractal: (2^2*n)*((2^n+2)+3) (A062709)

2nd Basketbox Fractal : (2^n+1)^2*7(2^n+1) 135, 725, 4617, 32,657.... (A083686) 4/28/2020

Square-Star Series: 4*(3*n*(n+1)+1) Centered Square minus its Hexagram. The interior contingent hexagon is reiterated fourfold in each corner of the square.

Logos Series: 12*(5n² + 5n + 1) +1 13 hexagram/6 hexagon

OR Starhex Honeycomb: a(n) = 13 + 60*n + 60*n^2, (A332243) 1st published series 5/16/2020

Hoarfrost Series 18*(5n² + 5n + 1) +1 13 hexagram/6 centered squares

Tristar Series: 3*(7n² - 7n + 1) + 1 3 hexagram/1 hexagon

Spiral Star Series: 6*(7n² - 7n + 1) + 1 7 hexagram

Starframe Bipyramids: 2*(3n+2)^2 + 3 Diamond shaped (bipyramidal) hexagram frames based on 3n+2 (A016789)

STAR RHOMBICS (Hot Air Balloon Numbers): 2*n*(2*n^2-1) These are mating pairs (male & female geometry that fit together) that give birth to twin stella octangula.

What's really interesting about these 'Hot-Air Balloons' is that they work either direction, where the balloon lifts the basket or the basket pulls down the balloon. In either event the result is the same two stella octangulas: 15-13=1+1, 65-37=15+13, 175-73=65+37...

Pseudo-Cubes: 6*(n*(2*n+5)*(n-1)/6)+1 These contain a six-fold geometry of square pyramids minus 1n. (A051925)

Centered Starframes: 18*n - 5, n>0 Every third star number will also be a centered starframe number, where n = centered hexagonal number. Almost all numbers are either prime or semi-prime or triprime. Starframes are typically formulated as (A019557) or here: (18n-6)+1. By adding a surrounding hexagram perimeter you get 30n+6 (A139249) Biblical 'N's are: n(21) = 373, n(22) = 391, n(37) = 661 (Star#11), n(51) = 913, n(391) = 7033 (13x541), n(2368) = 42,619 or (391x109) & n(1)n(2) 3x3x13x31=3627=John1:1

Nesting Starframes: 54*n+6 If both are considered whole stars and we subtract the interior star we get twelve times the pentagonal numbers: 12(n(3n-1)/2) or pentagrammic hexagrams see below.

Married Nesting Starframes: 54*n+36 This is the opposite parity starframes which meet at six points on the hexagon.

Star Badge Numbers: 6*(n+(n+1)^2)+1 These are (A028387) times six plus one.

Davidstars: 6*n^2+19 These are six times n^2+3 plus one (A117950) Each iteration increases by 12n+6 (A017593)

Concentric Odd-Star Perimeters: 12*n*(n-1) (A064200), i.e. 1, 1+24, 1+24+48...

Concentric Even-Star Perimeters: 12*n^2, (A135453) i.e. 12, 12+36, 12+36+60... These numbers are perfectly reflected in hexagrams made of triangular cells, where each equilateral triangle of cells equals a perfect square. The missing units are centered 24 gonal numbers (A069190) 1,25,73,145.. . Centered Hexagonals alternate similarly with 6n^2 and the Star Numbers, 13, 37, 73... .

Pentagrammic Hexagrams: 12*(n*(3*n-1)/2) These are centered dodecagons (A003154) (2n - n) and twelve times the pentagonal numbers. Also the partial sums of every other starframe (12+48, 12+48+84, etc.). The centered hexagonal center is 6x pentagonal numbers and either triangle is 9x pentagonals.

Hexasexagrams: 126*n+72 These are also 18*(7*n+4) (A017029)

Starburst Starframes: (108*n^2+60*n+24)/2 Joined starframes, also formulated as (A277983) 54*n^2-78*n+36, for n>0.

Star-of-Starframes Daisy Chain: 72*((3*n+2)*(3*n+5)/2) Each hexagram perimeter is 18n-6 (A019557) multiply each entry by the next. Also 18*(n*(n+1))-6.

Star of Stars Daisy Chain: 12*(n^2*(3n^2-2))+1 These are the square indexed octagonal numbers (A000567) times twelve plus one. The second is 2701.

Triskelion Hexagrams: 84*(n*(n+1)/2))+1 These are 84 times the triangular numbers plus one (A000217) These numbers appear to be always semi-prime.

Triskelion Hexagram Frames: 18*(7*n+4)+6 (A017029)

Jerusalem Snowflakes: 72*(n*(n+1)/2) Triangular numbers times seventy-two. (A000217)

Each additional ring of stars (minus overlapping points) equates to a 72n multiple of the triangular numbers, ad infinitum. This is probably due to the fact that Star(N) minus Star(N-2) = 36n and hence Star(N) minus Star(N-4) = 72n, i.e. 73-1=72; 181-37 =144, 337-121 = 216... etc.

Octagonally Squared & Squared Octagonal Numbers: (n*(3*n-2))^2 octagonally indexed squares & n^2*(3*n^2-2) Octagonal numbers with square indexes

Hexenstar Series: 6*(5n*(n-1)) + 1 3 hexagram/4 hexagon

Tetractys Star Series: 3*((4n+1)*(4n+3)) + 1 6 hexagram/4 hexagon

Stellahex Series: 6*(2n+1)² + 1 & 60*(2n+1)² + 1 & 168*(2n+1)² + 1 & ad infinitum

Daisy-Chain Frames: 2^5*((3*n+1)*(3*n+5)/2) These shortcut to the fifth multiple of two and (A178977).

The evens only 2^6*(3n+1)*(3*n+4) (A085001)

Starhexen Series: 12*(25n(n+1)/2 + 3)) +1 13 hexagram/24 hexagon

Star-Ring Series: 12*(3n-1)*(3n-2)/2) 6 hexagram/6 hexagon

Hex-Ring Series: 2*(6n+3)² 6 hexagram/12 hexagon

Jubilee Series: 12(49*(n*(n+1)/2)+6) + 1 25 hexagram/48 hexagon

The Honeycomb Hive (fractal): 6*(n^2*(3*n^2-1)/2)+1 Centered hexagons N*N+1 or six times pentagonals (A260810) with square indices

These numbers can also be represented by nesting diamond-frames (octahedron-frames)

Hourglass Numbers or the Boxcube Series: 2*(3*n² + 2)

Ribbon-box: 24n - 6 Also six times every other odd number or 6*(4n+3) (A002145)

Ribbon-basket: 144n + 18 This is also 18*(8n+1) (A017077) Eliminating the central axis produces 8*(12n)

Platonic Super Form: 4*(13n² + 2) + 2

Platonic Super Form: 10*(9*n+5) All 5 Platonic frames together in every 3rd dodecahedron frame (A017221) And the digital root of all these integers is 5!

Every 7 iterations of all 5 frames reproduces the Master Mold Dodecahedron (M.M.D.) at 70*(9*n+5) or every 3rd MMD and alternating the rows alternates MMD's. Of these, every fourth (4n) dodecahedron frame is also a cubeframe and a tetractys of cubeframes (x10). Cubeframes that are dodecahedron frames formula: 120*n + 80.

Five-Form Coefficient: 5*(9*n^2-17n+9) Partial Sums of All Five Frames: Each frame-shape = (9*n^2-17n+9)

Coefficient Geometric Series: 3²+2, 6²+3, 9²+4, 12²+5, 15²+6, 18²+7, 21²+8....

Dual Frame Form: 48*(2*n+1)+6 This is basically 48 times the odd numbers. OR 6*(16*n+8)+6 The sum of all geometric platonic dual forms (icosahedron&dodecahedron, octahedron&hexahedron, tetrahedron&tetrahedron) The 16n+8 series (A051062) is the first cube times the odd numbers, which creates an infinite cubing of all their divisors. (A173080)

House Frame Numbers: 8*(2*n+1)+1 Add One to the 16n+8 series and you get the frames of house numbers (A051662) 1,9,25,41,57,73...

Dual Surface Points: 54*n^2+12 This is six times 9n^2+2 (A010002) or 6*(9*n^2+2) The sum of all geometric platonic dual surface point forms (icosahedron&dodecahedron, octahedron&hexahedron, tetrahedron&tetrahedron) The average of each are (A010002).

Dual Solid Forms: 6*((n*(n*(3*n+7)+6)+2)/2) The sum of all geometric platonic dual solid forms (icosahedron&dodecahedron, octahedron&hexahedron, tetrahedron&tetrahedron) The average of each are tricapped prism numbers (A005920) which are cubes (n^3) plus pentagonal pyramids (A002411)

Master-Mold: 20*(18*n+1) Every 12n+1 dodecahedron frame, sum of all five 20 Platonic frames (A161705)

MasterMaster Mold: 100*((5n+4)*18)+1 Every 5 Master-Mold dodecahedron frames (A016897)

7-Fold Frame: 10*(7*(3*n+2)) Sum of every 7 dodecahedron frames = every 7n+6 dodecahedron frame, plus 210 per (A016789)

Infinite Frame Form: 10*(n*(9*n+1)/2) Partial sums of all five Platonic frames (A022267) where n*(n+1) are Pronic Numbers and n*(n+1)/2 are Triangular Numbers. Four times the triangular numbers plus the heptagonals. The terminal repeat cycle sums are: 90, 10100, 991,000. The 200-digit binary cycle is the 100th pronic number (100x101).

Natural numbers triangle spoke 0, 5, 19... x1

15

/ \

16 14

/ \

17 3 13

/ / \ \

18 4 2 12

/ / \ \

19 5 0---1 11

/ / \

20 6---7---8---9--10

Cubic Repeat Cycle: (1+2+3+4+...+9)*10n

Icosahedron Frame: 6*(5*n+2) (A016873) Also 30n-18, Icosahedron vertices = 12, edges = 30

Icosidodecahedron Frame: 10*(6*n+3)+2 (A016945) (Dual geometry Icosahedron + Dodecahedron Frames)

Compound Cube/Octahedron Frame: 24*n+14 or 12*(2*n+1)+2 This formula (A142241) is 12 times the odd numbers plus 2.

Compound Tetrahedron Frame: 12*n+2 Joined tetrahedron frames -6 points of union, also cube-frames -6, since 1/2 a cube-frame equals a tetrahedron frame.

All Pyramids: n^3 = n!/(n-3)!+n*(3*n-2), n>2 See (A007531) Nexus Cubes or All-Pyramid geometry has a connection to factorials, the multiplication of all integers symbolized by n!. Six times the tetrahedrals (which alternate parity with step pyramids) complete a cube with nexus formation of the octagonal numbers.

If we reset the pieces so that the tetrahedrons inserts begin at 5^3, the formulas alternate parity as ODDs= 4*(9*n^2-4*n+2) or (A086640) x 4 , EVENs = 8*(9n^2+5*n+2/2) or (A064225) x 8

{w,x,y,z} (A212133) Twice each minus one equals rhombic-dodecahedrons.

If we replace the above triangles with the triangles that are the hexagonal numbers, the side length will 4n+3 and the interior void-cube will be 2n^3, the even cubes.

Nexus Nesting Cubes: Odd/Even Octagonal Numbers (A000567) produce 'Nesting Cubes' made of odd/even cube-frames

Multiplying these together creates cubic partial sums of the dodecahedral numbers (A116689)

Should we multiple the even octagonal numbers by the even dodecahedrals numbers a pattern emerges that was hidden between the two of them revealing the pentagonal numbers times four squared: (4*(n*(3*n-1)/2)^2*(12*n+10) Pentagonal #s (A000326) & 12n+10 (A017641) [8x20, 40x220, 96x816, 176x2024, 280x4060, 408x7140, etc.] If we do this then with the odd octagonals and odd dodecahedrals another pattern emerges, that squares the odd octagonals, revealing a deep kinship in the multiplicities of the two: ((2*n+1)*(6*n+1))^2*(3*n+1), odd octagonals times 3n+1 (A016777), please note this is the exact formula for the odd dodecahedrons with the octagonal portion squared: [Odd Dodecahedrals: (2*n+1)*(6*n+1)*(3*n+1)] The formula 3n+1 is the basis for one corner of cube-frame, so multiplying it by the eight corners of the cube creates cubic-dodecahedrons below:

Cubic Dodecahedrons: 8*(n*(3*n-1)*(3*n-2)/2) Frames and Nesting Frames are fundamentally linked with the dodecahedral numbers (A006566).

The nexus nesting cubes (above) are a compressed version of below. Telescoping them out produces cubic-dodecahedrons.

The connection between cube-frames and cubic nesting frames comes about because dodecahedral numbers are the alternating product of the odd cube-frames and the odd nesting frames (odd octagonals numbers). ODD Dodecahedrons = (3*n+1)*(2*n+1)*(6*n+1) or 3n+1 times odd octagonals; EVEN Dodecahedrons = (6*n+5)*(n*(3*n-1)/2 or 6n+5 times pentagonal numbers. Because of this, everytime we multiple the dodecahedral numbers by an even cube of itself it creates a new series of nesting cube-frames, e.g. 4^3 x Dodecahedrons = Even Cube-frames times Even Octagonals or 32x40, 56x96, 80x176, 104x280, 128x408, 152x560, 176x736... .

The connection between these two series (Nexus Nesting Cubes and Cubic Dodecahedrons) has a profound geometry that is modular and telescopic, where the partial sums of the cubic-dodecahedrons becomes Nexus Nesting Cubes, where the empty frame geometry compresses into hybrid Nexus Nesting Cube, with the same sums but different dual geometry per iteration:

Collapsed or compressed modular cubic-dodecahedrons

Odd octagonals times odd cubes coalesces the factors producing the elegant (and hyper-dimensional) odd-numbers to the fourth times 6n+1. (2*n+1)^4*(6*n+1). Performing this operation on the even cubes and even octagonals produces rings that are multiples of eight and the difference between odd squares (aka the centered octagonal numbers) which then multiple by the cube-frame series. This is due in part to the fact that the octagonal numbers are byproducts of the odd squares (3^2 - 1^2 = 8, 5^2 - 2^2 = 21, 7^2 - 3^2 = 40...).

NestingNesting Cubes: (2*n+1)^2*(6*n+1)*(16*(n-1)^2-16*(n-1)+1) These are the odd numbers squared times 6n+1 times centered 32 gonal numbers. OR odd octagonals times cube-shells within cube-shells. [21x99, 65x485, 133x1351...]

Hyper-NestingNesting Cubes: (n*(9*n^3+6*n^2-5*n-2)/8)*(16*n^2-16*n+1)*(2*(n-1)+1) These are the partial sums of dodecahedrons (A116689) times centered 32 gonal numbers times the odd numbers (n-1) OR shells within shells of nexus nesting cubes. [99x168=16,632, 485x840=407,400, 1351x2600=3,512,600...]

Octanest (Octagonals x 8): ODD 8*(2*n+1)*(6*n+1) Odd#'s (A005408) OR 32*(n*(3*n+2) Rhombic Matchstick #s (A045944)

EVEN: 64*(n*(3*n-1)/2) Pentagonal #s (A000326)

Amputated Odd Ordered Rhombic Dodecahedrons: 32*n^3 + 8*n + 1, These are eight times the even magic constants plus one. (A317297) or 8*(n - 1)*(4*n^2 - 8*n + 5)+1 or simplified 8*n*(4*n^2+1)+1

Rhombic Dodecahedron Frames: 24*n + 14 The four angled sides of a pyramid times 6 plus the eight corners of the cube. (A142241)

OR Strong Version: 12*(3*n+1)+2 or 36n - 22 Including the frame of the interior cube.

OR Double Strong Version: 10*(6n+5) = Odd Dodecahedron Frames (A016969) [Cube-frame] + [6 x square pyramid frame]

OR: Double Strong Surface Points: 6*(1+n+2n^2)+2 (A084849) = the integers plus the integers squared, times two, plus one.

OR: Double Strong Nesting Frames: ODD: 10*(n*(6*n-1))+1 The even pentagonals (A049452) times ten plus one.

EVEN: 10*(2*n+1)*(3*n+1) - 2 The odd pentagonals (A033570) times ten minus two.

Rhombic Dodecahedron Nesting Frames: ODD: (2*n+1)*(12*n+1) (A033576)

EVEN: 2*n*(12*n - 5) The even 14-gonal or tetragonal numbers. (A270794)

Tetrahedral Nesting frames: Due to the tetrahedron's specific geometry they iterate four frames and shells, i.e. they nest every fourth.

1st Iteration: 2nd Pentagonals times two, minus one (2*(2*n+1)*(3*n+1)) - 1 (A033570)

AND 2*n*(6*n+5) These are twice the 2nd 14-gonal numbers (A211014) plus one.

2nd Iteration: 4*n*(3*n-2) These are four times the octagonal numbers (A153794)

3rd Iteration: 2*n*(6*n-1) (A126964)

4th Iteration: 8*(n*(3*n + 1)/2) These are eight times 2nd pentagonal numbers (A005449)

Tetra-cubes and Tetra-diamonds: (n-1)*(7*n^2-11*n+6)/6 (A185788) & n*(5n^2+3n+4)/6 (A203551) tetrahedrons plus cubes and tetrahedrons plus octahedrons. All four (tetrahexatetraoctahedron) together: 2*(n(n+1)/2 + n^3) (A085786)

Diamond-Cubes: n^3+(n*(2*n^2+1)/3) This hyperdimensional dual geometry (hexahedrons+octahedrons) is twice (A006322) i.e. 5*(1+2+3+4+5)+4*(2+3+4+5)+3*(3+4+5)+2*(4+5)+1*(5) gives (75+56+36+18+5)*2 = 380

Dual Dodecahedrons/Icosahedrons: 2*n*((7*n^2-7*n+2)/2) double c. heptagonal prisms (A329530) or (n*(3*n-1)*(3*n-2)/2)+(n*(5*n^2-5*n+2)/2) (A006566) + (A006564)

Square Pyramid Nesting Frames: These alternate parity without a center:

ODD: n*(8*n+5) Found on the square spiral. (A139277)

EVEN: n*(8*n - 3) Found on the square spiral opposite above. (A139273)

Icosahedron Nesting Frames: ODD: 6*(n*(2+5*n)) Six times (A168668) 5/13/2020

EVEN: 12*(n*(5*n-3/2)) Twelve times the heptagonal numbers (A000566) Vertices times 7-shape

Dodecahedron Frames: ALL: 10*(3*n+2) (A016789) ODD: 10*(6n+5) (A016969) Even: 10*(3*n+1) (A016777)

Dodecahedron 'Nesting' Frames: ODD: 10*(n*(3*n+2))+1 Ten times Rhombic-matchstick numbers plus one. (A045944) 5/13/2020

85--84--83--82--81--80

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56--55--54--53--52 79

/ . \ \

57 33--32--31--30 51 78

/ / . \ \ \

58 34 16--15--14 29 50 77

/ / / . \ \ \ \

59 35 17 5---4 13 28 49 76

/ / / / . \ \ \ \ \

60 36 18 6 0 3 12 27 48 75

/ / / / / / / / / /

61 37 19 7 1---2 11 26 47 74

\ \ \ \ / / / /

62 38 20 8---9--10 25 46 73

\ \ \ / / /

63 39 21--22--23--24 45 72

\ \ / /

64 40--41--42--43--44 71

\ /

65--66--67--68--69--70

EVEN: 20*(n*(3*n-1)/2) Twenty times pentagonal numbers (A000326) The number of vertices times its polygon face.

Snake-Eyes Series: 2*(12n + 1)

CrackerJacks: 8*(8*n^2-6*n-1)+1 Or eight times these (A194431) plus one.

Christ's Snowflakes: 10*(6n+1)-15 or 60*n+55 or 5*(12n + 11) in which all iterate snowflakes after the initial term of 11. 5*(A017653)

Discovery of Bill Downey (www.thesecretcode.co.uk) who calls them: Christ's Snowflakes.

Starry-Star Series: 12*(13n² - 13n + 2)/2) + 1

The Starless Triangle: a(n) = n*(4*n+1) Subtract a fitted hexagram from its triangle, remainder equals (A007742)

Disciple's Star: 12*(n*(n+3)/2) Hexagram minus its 13 center (A000096)

Star-Diamond Series: 10n-1*(n*(n+1)/2) Every 9 repdigit triangle (A002283) x (A000217) Digital sum of the stella-octangula/octahedral repeat series

Vessel-boxes: 8*(n*(5*n-1)/2)+1 These are the surface points of a cube minus one side. Also eight times (A005476)

Jewelry Box Numbers: 8*(8*n^3 + 3*n^2 + n)/6) Odd centered cubes minus odd octahedrons

Chest of Drawers Numbers: 9(4n^2 - 10n + 7) (Odd Cubes) minus (Even Cubes x8) Divide by 9 and get NE spoke of Ulam's Spiral

The Intersection of Planes:

Perpendicular Intersection of Odd Squares: a(n) = (2*n+1)*(4*n+1) or (A014634) These are the odd hexagonal numbers.

Perpendicular Intersection of Even Squares: a(n) = 2*n*(4*n - 1) or (A014635) The even hexagonal numbers.

3D Hashtag Numbers, Perpendicular Intersection of Four Squares: 4*n^2 - 4*n or (A033996) These are eight times the triangular numbers. (0,8,24,48...)

36--37--38--39--40--41--42

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35 16--17--18--19--20 43

| | | |

34 15 4---5---6 21 44

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33 14 3 0 7 22 45

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32 13 2---1 8 23 46

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31 12--11--10---9 24 47

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30--29--28--27--26--25 48

\

3D Hashtag Numbers X3, Intersection of Six Squares: 6*n^2 - 9*n also 6x2 + 3x − 3

X4, Intersection of Eight Squares 8*n^2 - 16*n also eight times n^2 -2n (A005563)

X5: 10n^2 - 25n

X6: 12n^2 - 36n this is also 24 times (A000096)

X7: 14n^2 - 49n

X8: 16n^2 - 64n

X9: 18n^2 - 81n

Nesting Cubes: Nesting Cubes (Outer Shells) comes in four basic varieties based on the four possible centerpoints, two empty, two full (0,0 & 1,8).

Initial Cube 1^3 Center: 32*n^3+48*n^2+18*n+1; 1,99,485,1351 (A322830)

Initial Cube 2^3 Center: 8*((4*n+1)*(n+1)^2); 8,160,648,1664... (A103532) These are the divisors of 240^n times eight.

Initial Cube 3^3 Empty: (2*n+1)*((4*n+1)^2)+1; 26,244,846,2024... (A016813) Odd numbers times the double odd numbers squared plus one.

Initial Cube 4^3 Empty: (4*n+1)*(4*n*(2*n+1)-1)+1; 56,352,1080,2432... (A033586) & (A016813)

Alternating Nesting Cube-frames: As above these come in four varieties and each one is related to an established figurative number series:

YELLOW = 4x Second Tetradecagonals (A211014)

RED = 8x Octagonals (A000567)

GREEN = 4x Even Pentagonals (A049452)

BLUE = 16x Second Pentagonals (A005449)

YELLOW + GREEN = ODD Octagonals

RED + BLUE = EVEN Octagonals

Centered Cube Nesting Frames: 6*n^2 - 10*n + 5 (A136392) And partial sums of 12n+8 Cube-frames (A017617)

The opposite sum of the cube at its full dimension equals 6 times (A172482) (1+n)*(9 + 11*n + 4*n^2)/3

Alternating Double-Frames (8+20, 56+68, 104+116, etc.) = (12n+7) x (4n+1)

The remainder of the negative space of each cube = 6*((1+n)*(9 + 11*n + 4*n^2)/3) or SIX times (A172482)

9-Planes Cube: 4*(9n^2 - 6n +2) The intersection of nine even ordered squares (A185939)

This one may seem difficult to understand because so many of the squares overlap and the units are spaced one apart. Each above cube only represent 9 intersecting even squares. But because there are 9 EVEN squares that are spaced one apart they overlap in unexpected ways, very much like a interference pattern, e.g. for 20 = 2^2, 104 = 4^2, 260 = 6^2, etc... .

Group the natural numbers in sets of three. Multiple the first two and add the last, then multiple that by four and you get a 'Holy Cube.'

(1,2,3)

1 x 2 + 3 = 5

5 x 4 = 20

(4,5,6)

4 x 5 + 6 = 26

26 x 4 = 104

Etc.

Conjectures:

Three Cube Theorem: The sum of three consecutive cubes will always be a series of symmetrical squares centered on the sum of the bases.

The Multiple Gonal Conjecture: All centered gonal number series that are multiples of the basic geometric elements of a platonic solid (edges, faces and vertices) can be be arranged in 3D space according to said elements as sectioned by its triangular components.

The above graphic displays how the components of centered dodecagonal numbers can be arranged to fit with a nexus formation of a cube, the twelve triangles of the centered dodecagonals corresponding to the twelve edges of a cube.

Adding Star numbers to the C. Hexagonals that mate with them creates centered 18-gonal numbers 9*n^2 - 9*n + 1 (A069131), minus one for the shared center. Reducing the triangles by one iteration creates 9*n^2 + 3*n + 1 (A082040)

The Solomon Conjecture

The basic premise of the Solomon Conjecture is that all polygonal numbers (and their polyhedron bipyramidal equivalents) are based on the hexagram (Star of David).

The 3D version of this conjecture is that all polygonal bipyramids are based in the Rhombic Dodecahedron, the 3D equivalent of a centered dodecagonal number or a Star Number (hexagram).

The C. 10-gonal are also known as C. Icosahedral Numbers (A005902) which are seen here as representing 2/3 of a complete rhombic dodecahedron. They are also the centered cubes plus the partial sums of the even squares. (9+4, 35+20, 91+56....).

The basic elements in three dimensions are the square pyramid and centered cube, the basic components of a rhombic dodecahedron in three dimensions and the triangle and hexagon in two dimensions. Stellating the formation creates other hidden connections:

If we add eight more pyramids (one for each vertex of the cube) to the stellated rhombic dodecahedrons (the odd cubes) we get then the Odd tetrahedral numbers: 1, 35, 165, 455, 969 or (A015219) i.e. every fourth tetrahedron or an odd numbered tetrahedron. This are the tetrahedrons that terminate with star number triangles (every forth triangular frame).

If we continue the series so it is centered cubes plus 30 pyramids we get truncated octahedrons (A193228).

This is (A051925) times six plus which formulates both as six facing grooved pyramids (Sum n^2 minus n) and star-cubes with matching square pyramids.

John Elias

John Elias is an unlicensed and unaccredited Mathematical Archaeologist. This discipline employs mathematics and the science of probability to determine if ancient religious manuscripts were divinely inspired.

John Elias is a one-credit-short, college dropout. He is a long undiagnosed dyslexic. His least favorite subject in school was mathematics. He is the author of five unread novels, including this one (Poecraft) and hundreds of unread short stories and this Satire Site. He is of no denomination in particular. He is only Christian.

He studied at the University of Jerusalem College and dug at Ashkelon, Israel under the archaeologist Dr. Larry Steger of Harvard. He has studied the languages of ancient Egyptian (hieroglyphics), Sumerian cuneiform, Ancient Hebrew, Koine Greek, Latin, Russian and Japanese. He has invented several fantasy languages as well for his yet unpublished opus.

If you would like to contact him, email Johnelias@israelmail.com

The Mathematical Journey

By John Elias

Around seven years ago, I became interested an obscure field of study called Biblical mathematics. As you may or may not know, the Christian Bible was originally written, thousands of years ago, in Hebrew and Greek. The letters of both of these languages, also served as the numbers of these languages. This is called gematria.

The fact that every letter of Scripture is also a number, makes the Christian Bible the largest mathematical document of history. Considering that the Bible is the Holy Writ of the world’s largest religion and that mathematics is the basis of science itself, the possibility that a Divine Being might mathematically encode these scriptures was quite promising.

Having studied the ancient languages of the Mideast and the archaeology of the Bible, I was in a good position to investigate such a possibility. For five years I agonized over whether the patterns I immediately began to see, were just phantasms of my own imagination or in fact the fingerprints of God. In such a field as this, Confirmation Bias is a constant danger, yet patterns there were and they were multiplying.

I then began to notice a curious tendency: The more I looked for highly improbable mathematical patterns in the text, the more I found; and the more I found, the more highly improbable it was, that any of this could have ever happened by chance.

At last, I began to find patterns that were so shocking and so astronomically improbable, that collectively they constituted definitive proof that the Bible was Divinely Inspired. What’s more, these patterns were not only extensive and exceptionally improbable they were ubiquitous and could be found in every passage of Scripture.

It was then I decided to dedicate my life to revealing the mathematically Divine truth of the Holy Scriptures to the world.

What can be viewed on this website and in my videos represents only the topmost snowflake of the tip of the iceberg of how much evidence there is for this phenomenon. If you can imagine the Bible as the ocean itself, then the mathematical evidence for the Divine Inspiration of the text would outnumber all the fish and creatures of that ocean.

Most telling of all was, that I was not alone. Other scholars from around the world were making the same sort of discoveries as I. All of these mathematical discoveries were pointing to one big thing: God was real and the evidence of His Being was as abundant as the stars of heaven above.

The famous mathematician, philosopher and atheist, Bertrand Russel, was once quizzically asked, "What will you say to God if you see him after you die?" He retorted, "Not enough evidence Lord, not enough evidence." Well Bertie Old Boy, you were looking in the wrong place. Had you looked where He told you to look, in His Holy Word, you would have found more evidence than you could ever imagine.

God is real and the proof of His existence is exactly where it ought to be. It is found in His Holy Word the Bible, and it is proven by the very basis of scientific truth itself, mathematics.

John Elias

Want to get the latest discoveries in biblical mathematics? Then email johnelias@israelmail.com Subject Line: Updates!

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"Christianity has one thing that makes

it preferable to any other religion...

it's the best deal in the universe."

—John Elias