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Fibonacci Sequence: 60 Digit Cycle

First discovered by Jain-108!

See other Repeating Graphs in Formula for the Platonic Solids

Congratulations to Nigel! for finding the elusive 3D Fibonacci Repeat Cycle. AND he plotting it out using coordinates on a x, y, z grid! Check out the map to the Fibonacci 3D 'walk-about':

Fibonacci 3D Walk

The Lucas Numbers also have a graphing monocurve on a triangular grid:

Read about the Lucas Numbers monocurve

The first final terminal repeat cycle of the Fibonacci numbers displays a mind-boggling ability to return to its origin point. The discoverer of this fantastic feat (Jain-108) says that this shows the numbers to be intelligent. I personally cannot claim to know what that means, beyond rhetorical poetry, yet an apt description it is.

The numbers do this, not magically, but mathematically. Fibonacci number's are an additive series with very basic instructions, and all that addition leaves a pattern. The illustration above demonstrates the revolving process, where each number is a vector (direction). Because the repeat cycle has a zero every fifteen digits, the revolution itself revolves. And because the sum of all these vectors are equivalent, the path returns to origin.

The number of encapsulated squares is exactly 298

the sum of Genesis 1:1 in its alphabetic order (ordinal).

The Fibonacci Numbers and the 60 digit terminal repeat cycle:

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, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, 7778742049, 12586269025, 20365011074, 32951280099, 53316291173, 86267571272, 139583862445, 225851433717, 365435296162, 591286729879, 956722026041, 1548008755920, 2504730781961, 4052739537881, 6557470319842, 10610209857723

Most repeat cycles tested in this way (e.g. polygonal and polyhedral repeat cycles) either quarter-peat, requiring four cycles to repeat, or veer off on a severe southwest bias. Only Fibonacci related repeat cycles appear to have this graphing curve cycle. Numbers like (A013655) a Fibonacci Series from the Wythoff Array row 8, which is the sum of the Fibonacci and the Lucas Numbers, will reproduce the same graphing curve exactly, but starting and ending at different points. Indeed it appears the full infinity of the Wythoff Array will always display a perfect graphing curve of alternating either the 60 Digit 298 Capture or a 20 digit 88 Capture.

Wythoff Array 8 Repeat Cycle:

[2,5,7,2,9,1,0,1,1,2,3,5,8,3,1,4,5,9,4,3,7,0,7,7,4,1,5,6,1,7,8,5,3,8,1,9,0,9,9,8,7,5,2,7,9,6,5,1,6,7,3,0,3,3,6,9,5,4,9,3]

These simply jaw dropping features of the repeat cycles of Fibonacci and Lucas numbers is not only a perfect match for Genesis 1:1, it is also self authenticating. The sums of each encapsulated section (total: 298) can be reduced via digital summation. When we do so we get the number 127, an analog of the square root of phi, appropriately and very possibly 'coincidentally' enough.

This number however is seemingly programmed into the repeat series in a number of ways. This is what I call 'self-authenticating' because it is the number squares in the rectangle surrounding the formation.

Performing the basic arithmetic of digital summation

we miraculously arrive at the remainder of the container rectangle.

How do the numbers 'know' that

the remainder of their rectangle has 127 cells?

Further evidence is found in the index of all composite numbers (numbers with more than one factor).

As seen above, the ordinal first verse appears to also be aware of this rectangle, i.e. its language is programmed to correspond to the composite index of all integers with more than one as a factor. This being an index that is a product of the modern mathematical world.

By alternating the count of these encapsulated square graphing curve sections, based on its clockwise sweep, we find the alternation once more connects to 127, the closest decimal representation of the square root of phi, the golden ratio.

This is what I like to call impossible math. It probably shouldn't exist. In the mind of a materialist or atheist, these mathematical patterns cannot exist. And yet...

They exist.

The number of ways in which in this infinite configuration coordinates with the lettering of the first verse of the Bible is currently unknown, but it may be very large. Moreover, this split in the numbers (171/127) has a specific metaphysical and theological meaning, for the same split is found within the verse itself:

The meaning of the Hebrew would most likely be rendered "In the beginning God created—" or even 'In the beginning God.' (singular)

The grammatical importance of this specific split cannot be understated. Theologians have for centuries agonized over the meaning of the use of the word 'Elohim' in Hebrew. The reason it is so controversial, is that it is grammatically plural. By cutting off the final Mem 'M' in the word Elohim, it effectively converts the plural into the singular, i.e. Many Gods into One God.

The question is not: Why does this configuration separate into 171 and 127 in so many ways?

The question is: Why does it accord itself to this specific order of numbers?

The ordering of the squares and their numbers was not random, but based upon the 'logic of a spiral,'

where groups of squares are ordered based upon a clockwise rotation, spiraling out of the origin square.

The final transition shows how the order of the numbers can be digital summed into the remainder of the rectangle (17 x 25).

These sort of dynamic equivalences one might think are mathematical, that is explained by some deep mathematical logic. If it is, then it is deeper than any mathematics currently known to mankind. We must remember that these are not number per se, but sections of squares bisected by a spiraling curve. So in order for this to be mathematical logic, the sum of the squares of each section, must a calculated product of the cross-reference of the two-dimensional programming of each individual digits of the entire 60 digit repeat cycle. AND this programming can only come from the basic operation that creates the Fibonacci Series, namely repeated and summed addition.

This level of ingrained programming in simple numbers, is the sort of scientific mysticism reserved for science-fiction, like Carl Sagan's Contact. This however is real, infinitely real and referenced in the first verse of the Bible.

This it would seem is being highlighted, by the construction of the sentence and its interaction with the Fibonacci numbers. This we must remember is an infinite highlighting.

When we count the interior of this shape we find the exact opposite of what we find in the standard rendition of Genesis 1:1, namely the 216 sum (here the Shemhamphoresh proper) is now in the inside rather than the perimeter.

T-73 (2701) with highlighted 216 perimeter:

The infinite variety of infinite repeat cycles, it can be shown, are all based in the bountifully Biblical number 40. This no doubt has to do with the four elements of the repeat cycles, each of which sum to 20. Most likely it is the pairing of the odds and evens, leaving out the 5's and 0's as they are in independent arrays.

7^2 - 3^2 = 40

3^3 + 7^3 = 370

Fibonacci Double-Digit Cycle, 1-300 = 14,800 = 40 x 370

1-60 = 2880 = 40 x 72

61-120 = 3040 = 40 x 76

121-180 = 3160 = 40 x 79

181-240 = 2760 = 40 x 69

241-300 = 2960 = 40 x 74

40 x 370 = 14,800 = (7² - 3²) x (7³ + 3³)

The interior gray-whites units comes to 1080 the sum of the 'The Holy Spirit' in Greek.

The blue cubes number 40 each being 343 (7^3) while there are 40 gray-white cubes each numbering 27 (3^3).

This number 14,800 is highly coordinated with other biblical mathematical identities see the BIFRC

Fibonacci Triple-Digit Cycle, 1-1500 = 748,000 = 40 x 18,700

1-300 = 134,800 = 40 x 3370

301-600 = 156,800 = 40 x 3920

601-900 = 155,800 = 40 x 3895

901-1200 = 152,800 = 40 x 3820

1201-1500 = 147,800 = 40 x 3695

And within the 1500 triple digits there are subsets of multiples of 40 correlating with the former repeat cycle, ad infinitum.

within this:

1-300 = 134,800 = 40 x 3370

is this:

1-60 = 20,960 = 40 x 524

61-120 = 26,960 = 40 x 674

121-180 = 27,960 = 40 x 699

181-240 = 30,960 = 40 x 774

241-300 = 27,960 = 40 x 699

The entire infinity of infinite repeat cycles will always be a multiple of 40. If that repeat cycle is greater than an earlier repeat cycle, it will have a subset cycle, whose every member is a multiple of 40. If that subset has itself a subset, all its members will be a multiple of 40, on and on in finite regress, until it reaches to the base subset of 60 digits and 40 x 7 (280).

There are a number of very strange connections between the repeat cycles of the Fibonacci Series and the Breastplate of the High Priest, the ancient Jewish relic worn by the officiating priest of the Temple in Jerusalem. These are both connected via the star number series (13, 37, 73 etc.) since these numbers are, in point of fact, 12-based numbers (centered dodecagonal or 12-gonal). The breastplate of the high priest contained 12 precious stones, one for each of the tribes of Israel.

13 cycles of 45 fits within the 24 digit cycles as a star perimeter — the 13 little black triangles in the central star.

A full five-cycle of the 24 digital sum cycle is the equivalent of 13 cycles of the letters that describe the 12 gems.

The same full cycle of five-24-digits and/or two 60-digits creates a digital sum of 560 for the Fibonacci numbers, a perfect match for the ordinal sum of the 12 gemstones. Both 60-digit cycles creates octagonal numbers, the 10th (280) and again with the 14th (560).

One of the early achievements of biblical mathematics online community was tying together disparate passages to create a connected whole. Primary to this was the connection between Genesis 1:1 and John 1:1. The triangle of their union is an important piece of biblical mathematics history, but is only one piece of a much larger puzzle that connects these two verses. The other is in the John 1:1 Star-box which fuses the two verses in the six cardinal directions.

John 1:1 = 3627

In the Beginning was the Word and the Word was with God, and the Word was God.

Εν αρχηι ην ο Λογος και ο Λογος ην προς τον Θεον και Θεος ην ο Λογος

John 1:1 completes a larger triangle with Genesis 1:1

But it is in the two Fibonacci repeat cycles where the union of these verses is truly astounding. The two most famous repeat cycles of the Fibonacci Series is the 60 digit and the 24 digit. These are in way married to each other.

But what if we added them together?

This is, in a fashion, illegal math, out-of-bounds, verboten! since these cycles are integrated. But we will do it anyway, because when we do, the following configuration based on the breastplate of the High Priest becomes possible and illustrates the infinite connection between the verses as seen in the great canopy of heaven and in the whole tapestry of the universe itself.

Theses 120 numbers can be tiled from right to left, as Hebrew reads right to left, into the individual 'gems' of the breastplate configuration. When we do this the numbers coordinate together to form a pattern, a pattern that only makes sense when one knows some basic biblical mathematics's identities.

It takes five cycles of the 24 digit to equalize with the 60 digit.

24+24+24+24+24 = 120

60+60 = 120

Should we lay these out as a triangle (120 is T-15) we find a natural puzzle in Hebrew, who solutions must read something like the 'Spirit of Jesus.'

As has been proclaimed elsewhere (namely by Lucien Kahn) the 60 digit repeat cycle has an uncanny connection to the 72-fold name of God, the most revered numbered name of God to the mystical Jew. This 72 fold name is known as the Shemhamphoresh and was in fact a mystical configuration of the breastplate of the High Priest, as it was to be written out to represent 12 sections.

Lucien Kahn tiled the numbers on circles and began counting.

He overlapped six circles into a Star of David or Metatron's Cube.

By selecting only those numbers from within Metatron's Cube and placing them in the matrix of the Shemhamphoresh, the 216 Letter Name of God, equaled 60 across the board. Lucien believed this to be a signal event in the history of the world, perhaps even the dawning of a new age. And perhaps he is right. This was, however, not magic, but math.

How does the 72-Fold Name equal 216 letters?

The number 72 refers to the number of mystical compartments of the name, while it has 216 letters (3 x 72) three letters per compartment. And if you add in the angelic postscripts you get 288 total letters.

The repeat cycles of the Fibonacci Series, are highly encoded numbers in relative association or in a matrix, encoded by the process that produced them, 1+1+2+3+5+8... etc.. This terminal cycle is in fact organized on the number twelve (5 x 12 = 60) and should you play around with them in a spreadsheet you would find they would perform a number of marvels, all related to that number.

The connection between these numbers and the Shemhamphoresh is indeed profound and mathematically plain. Here we must remember that the Shemhamphoresh is composed of three verses from the book of Exodus, all with exactly 72 letters each, describing the very climax of the Israelite's flight from Egypt and the crossing of the Red Sea. According to the text and to Jewish commentaries and folklore these events were accomplished by God's agent, named the 'Angel of the Lord.'

The Angel of the Lord

מלאך יהוה

= 117

Each triple triangle of 117 comes to 351 or T-26, the 26th triangle, where 26 is the sum of the name of Lord (Yahweh). This correlates and connects with the 24-Digit Lucas Digital Repeat cycle which has the same sum of 117. Add them together, in anyway you want, and it reproduces this sum again and again forever, using the same operation of digital summation and anyone of the three 24 digit cycles: the Fibonacci, the Lucas and the Fibonacci/Lucas synthetic.

Fibonacci 24-Digit: 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9

Lucas 24-Digit: 1, 3, 4, 7, 2, 9, 2, 2, 4, 6, 1, 7, 8, 6, 5, 2, 7, 9, 7, 7, 5, 3, 8, 2

Fibonacci/Lucas 24-Digit: 2, 4, 6, 1, 7, 8, 6, 5, 2, 7, 9, 7, 7, 5, 3, 8, 2, 1, 3, 4, 7, 2, 9, 2

If you add the Fibonacci 24 Digit to itself, the digital root result will always sum to 117.

If you add the Lucas 24 Digit to itself, the digital root result will always sum to 117.

If you add the Fibonacci/Lucas 24 Digit to itself, the digital root result will always sum to 117.

And if you add any of these resulting 24 digit summations to themselves or those to themselves, etc. etc., ad infinitum, or add former iterations back into the equation they all will always sum back to 117.

So the number 117 is the magic number to the endless repetitions of the Fibonacci and Lucas Numbers. And this magic number we find in magic places. The Shemhamphoresh Sierpinski fractal is pattern is reiterated in the decimal expansions of phi and e at the three-thousand-one-hundred-and-sixty-eighth decimal place, the proper reading for the name the Lord Jesus Christ in Greek (3168).

All three of the most important irrational numbers in mathematics display significant and unusual organization at the number that represents the highest theology of the world's most popular religion.

The same 216 (72 x 3) letters that produce the holy name fits very well within the confines of the repeating triangle of its own sum.

The Sierpinski arrangement is further evidence by the fact that the Shemhamphoresh Sum (3159) performs equally well as a series of triangles, each being the 26th (351) a singular connection to the name of the Lord, the Tetragrammaton, the most reverenced name of the God, and the basis of the entire elaboration of the Shemhamphoresh configuration.

What's truly compelling is how the negative space of this configuration (5460 - 3159 = 2301, where 5460 is T-104) is the 26th nonagon, or 9-gonal geometry. Such coordination strongly suggests engineering.

The letters of the Shemphoresh itself also coordinate with the Sierpinksi pattern:

(The angelic postscripts Yah and El, seen in the lowest row of each section, are what you might call 'optional'. That is to say, they are not the proper name but the proper name would not be complete without them. In other words, they are both part of the historical creature that is the Shemhamphoresh, and one cannot choose one or the other, both must be considered within the equation.)

We can configure these in another fashion using star-triangles (every 4th triangular perimeter) and we find an even more elegant and 'Christian' configuration.

When we employ distributed tiling on the Metatronic numbers (those numbers specially extracted by Lucien Kahn), we can see that they are governed by the number 12 and readily coordinate to the sum of 90 per block.

If we employ a similar distribution system but now tile the Metatronic numbers into the 6th cube, we find a rebus puzzle based on the Hebrew gematria of the Spirit of God (300) and the proper Hebrew title for the Lord Jesus Christ (780).

The solution to this puzzle (and one we've seen elsewhere) is that the Holy Spirit (300) was inside the human vessel of the man known to history as Jesus Christ (Lord Jesus Christ-780).

The key feature of the Fibonacci repeat cycle is the digital sum (280). This number is deceptively simple and hosts a wide range of mathematical connections. One of the most intriguing is that of the octagonal numbers (numbers produced by repeated iterations of an octagon, an eight sided shape). Both the 60 digit cycle and its double are even ordered octagonal numbers (280 and 560 = Oct-10 & Oct-14). Octagonal numbers, being based on the first cube (2 x 2 x 2) are highly organized and three-dimensional.

Both odd and even octagonal numbers reproduce Nesting Cubes with infinite fidelity.

The Reciprocal of 298

148 repeating decimals (37 x 4) with a digital sum of 666

1/298 =

0335570469798657718120805369127516778

5234899328859060402684563758389261744

9664429530201342281879194630872483221

4765100671140939597315436241610738255

0335570469798657718120805369127516778 = 178

5234899328859060402684563758389261744 = 183

9664429530201342281879194630872483221 = 155

4765100671140939597315436241610738255 = 150

Red = 333

Black = 333

Total = 666

03355704697986577181208053691275167785234899328859060402684563758389261744

+ 96644295302013422818791946308724832214765100671140939597315436241610738255

= 99999999999999999999999999999999999999999999999999999999999999999999999999

The 12 Flavors

The 60 digit repeat cycle can be shown to operate in 12 flavors of the four elements. The tiling begins in the upper left hand corner and descends into a column of 12 cells. The next iteration advances the pattern one. By doing so we can observe that this 12 column coordinates with the base-10 number system producing a repeatable pattern.

The Fibonacci Numbers and the 60 digit terminal repeat cycle:

Follow the numbers down each column, in each rectangle. The rectangle in the upper left hand corner begins 1, 1, 2 and down. Each new rectangle advances the numbers one position.

The numbers highlighted in yellow are all the same five even integers: 0, 2, 4, 6, 8

We could continue the iteration, but the arrangement would only differ in the columns and not the sums. This is the maximum pattern of the 60 digit cycle.

60 digit + 24 digit = 84

12-Cycle x 12 = 3360

40 x 84 = 3360

It is unknown whether the above fact is coincidental or causative.

If we multiply all the 24-Digits of the Digital Root cycle together we get number over 67 trillion:

Fibonacci 24-Digit: 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9

1 x 1 x 2 x 3 x 5 x 8 x 4 x 3 x 7 x 1 x 8 x 9 x 8 x 8 x 7 x 6 x 4 x 1 x 5 x 6 x 2 x 8 x 1 x 9 = 67,421,129,932,800

3360² x 144³ = 67,421,129,932,800

The fact that this can be expressed so simply, belies the fact that it represent an army of various figurative geometries, best typified by star numbers, simply because star numbers are indeed centered dodecagonal numbers, that is numbers that increase by 12 and factors of 12 around a center point. In other words, Fibonacci Numbers and the various repeat cycles are multiplicities based on the number 12, a number a nature appears to favor for sheer multiplicity.

The 67 trillion number can be divided by the digital sum of the 60-digit cycle (280) hence representing over 240 billion cycles.

67,421,129,932,800/ 280 = 240,789,749,760

The 216th Fibonacci number shows an interesting correlation to the 216 metatronic numbers, in that it adds up to 216 and is the 9th triangle of digits, a triangle composed of the 9 cardinal numbers.

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1 9

2 2 0

4 5 1 6

6 6 5 9 0

1 3 5 2 2 8

6 7 5 3 8 7 8

6 3 2 9 7 8 7 4

2 6 9 3 9 6 5 1 2

Fibonacci #216 619220451666590135228675387863297874269396512

6+9+2+2+0+4+5+1+6+6+6+5+9+0+1+3+5+2+2+8+6+7+5+3+8+7+8+6+3+2+9+7+8+7+4+2+6+9+3+9+6+5+1+2 = 216

A careful examination of the sequence shows that the number of digits in a Fibonacci Number doubles (within a fraction of a percent) every 216 numbers.