Fibonacci Numbers

The Fibonacci Circuit: an infinite 3D loop corresponding to the 12 edges of a cube.

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The Fibonacci Repeat Cycle System

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The Fibonacci Numbers (and the related Lucas Numbers) are some of the most famous and pivotal number sequences in the history of science. They are intimately related to so much of the science of the natural world and the great classical concept called the Golden Ratio, known also as the Logos in the original Greek, that they have become the poster-child of science memes on the internet.

There is a terribly-interesting-and-almost-unknown-fact about these numbers, and this terribly-interesting-and-almost-unknown-fact permeates the entirety of these numbers in a system of nesting patterns that has infinitely many nests. This is the infinitely repeating and infinitely complex repeat cycle system and it is a very much an unstudied aspect of the Fibonacci Numbers.

That is until very recently, when it was discovered (first by Jain-108, then here @37x73.com and lately also by Nigel Fisher) that many of these number cycles have corresponding repeating geometries, now found in three and higher dimensions.

Below you see an aggregate or simplified version of the process, where the digits of the repeat cycle are translated as vectors or lengths of the specific dimension traveled. By putting the numbers in a table of twelve rows, one row for each of the edges of the cube, you discover a Fibonacci Circuit, an infinite cycling of the numbers in three dimensions.

This Fibonacci Circuit is a much simplified version of the actual individuated travel vectors, see below. But this elegant design corresponds to one of the most stunning evidences found in the gematria of the Bible, a fact and feature hidden in the name of the Lord God.

The Fibonacci Circuit outlines a cuboid of 26 x 46 x 46, this rectangular structure is a geometry of gematria made in heaven.

Thanks to Jain-108, who not long ago had a completely-out-of-the-blue epiphany, when plotting out the Fibonacci 60 digit repeat cycle on a piece of graph paper, realized that it returned to its point of origin. These 2D Walks have been explored at length here in 60 where the plot creates a map of Genesis 1:1 and here where the patterns in the Lucas Numbers are explored.

Recently, however, Nigel Fisher contacted me with a grand new breakthrough in the Fibonacci Repeat System. Working off the 2D maps, he plotted out the 3D paths of the 60 Digit Fibonacci repeat cycle. In mathematics, these patterns are called 'Walks' and below is the link to the spreadsheet with the exact coordinates of both Fibonacci Walks in the three dimensions.

Fibonacci 2D & 3D Walks

Below is an animation of the Fibonacci 3D Monocurve. These numbers return to origin because the opposing x, y, z dimensional vectors are equivalent (i.e. height, breadth & depth). By organizing the numbers into six columns, where each column represents a direction (or vector) on a 3D grid, one can see that vectors find ultimate equivalence and thus return to origin to repeat the pattern perpetually.

This is the same pattern of the Fibonacci Circuit seen above, i.e. the distance in each dimension traveled is exactly the same, only here it appears all jumbled.

The zeroes in this walk are turn-styles only, changing the vector's direction, not advancing it.

The perimeter of this the Monocurve Path is 21 x 22 x 22 or 10,164. All the graphing curves discovered so far in three dimensions create this type of cuboid where two of the dimensions will always be the same. What's fascinating about this space, is that it is a star of stars, filled with biblical mathematical possibilities (like the two Messiahs, 363 & 726, Hebrew & Greek (28 x 363 & 14 x 726)).

10,164 (84 x 121)

The first terminal repeat cycle of the Fibonacci Series can repeat to origin in two different ways, using standardized procedures. The difference and the reason for the difference is the number (or lack of number) in zero. Monocurve mapping is basically treating the Fibonacci numbers as a set of vectored coordinates. Because the reverse vectors are exactly equal to the forward vectors the monocurve returns to origin. Zeroes, in this schema, however do not travel they only change the vector's course.

The question occurs: What would happen if you throw out the zeroes?

The animations above includes the zeroes, as turn-styles only, the animation below omit the zeroes altogether and displays a return to origin after a triple repeat (a tricurve).

The fact that the series completes both a monocurve and a tricurve is noteworthy and deserves further study. Due to the exponential nature of the Fibonacci Numbers it is currently beyond the calculating abilities of 37x73.com to analyze most of the larger repeat cycles, nor is it known if there is a standard walk by which all cycles conform.

This tricurve intersects its own path in many places, highlighted by the off-colors in the image below:

What is really mindboggling about this Fibonacci tricurve is how it connects to one of the biggest finds in the history of the biblical math of pi. The tricurve is a 3D repeat of the terminal Fibonacci-60 repeat cycle three times over:

Fibonacci-60 = 280 cycle sum

280 + 280 + 280 = 840 = Perimeter of the 70th Star in Pi

The GIANT Christian Cross of Fibonacci

The Fibonacci Repeat System gets really large, really fast. From the initial 60 digit terminal cycle, it then goes to a 300 cycle of double digits, and then onto a 1500 cycle of triple digits. After that it goes, 15,000, 150,000, 1,500,000 on and on. Since these cycles are made up of individual numbers (like the 1.5 million cycle is 1.5 million six-digit numbers) these cycles sums become exponentially large.

The largest one available where we have every individual number individuated into cells, is the three-digit Fibonacci 1500 (see bottom of the page for the spreadsheet download). The cycle sum for the Fibonacci-1500 is 748,000, making it a multiple of ten cubed, which offers a perfect unit for a greater expression. The number 748 is one of the newly discovered 'Cross Numbers' which are numbers that graphically and mathematically produce a cross. The important part being the 'mathematical' part, where cross numbers are the product of four 2nd pentagonal numbers, each one being one of the four arms of the cross.

That means the Fibonacci-1500 is a giant mathematical cross.

Click to ENLARGE

The famous NT phrase 'The just shall live by Faith', quintessential to Christian theology, was actually a quotation of the Apostle Paul from the OT book of Habakkuk. The literal Hebrew here reads, 'But the righteous (one) shall live by his faith.' The manifest Christian symbolism here couldn't be any more obvious or theologically on-the-nose, the just shall live by their faith in the cross of salvation.

This cross configuration is actually very much indicated in the cycle itself, where every 4th row is the sum 187,000, i.e. a cross arm of the giant cross itself. Cross numbers are something the gymnast of the mathematical world, because they are 2nd pentagonal numbers times four. First and second pentagonal numbers are one of the increasingly important unrecognized stars of mathematics.

There are the two components that make up a centered hexagon found at the center of the ubiquitous star numbers. Because 1st &2nd pentagonals are themselves made up of portions a triangle, they are like connector-lego-bricks that tie many other maths together.

But cross numbers also form a cube, which is nothing more than an alternating series of cube-frames. What's amazing about these numbers however is how they marry to the star numbers:

It is fair and quite literally fair to call this configuration a Christian Cross, being that it spells out the original word for Christian precisely.

There is something very mysterious going on with this number (1541) because it agrees in essence (134k & 1541k are multiples of 67) with the sum of the Lucas Number for their 3-digit cycle, with every other cycle and in other multiples:

Fibonacci 1,000-Fold Star (1,541,000) x 10 = Lucas Number 3-Digit Cycle (134,000) x 115

The make up the 12th star number contains the math of the Three-Seven Code, as typified by 37&73, here it is 397&793 with the synthesis in each triangle being 595 (five being the average of 3+7). We see this exact same pattern in the 37th-Star (featured so prominently in the decimal expansion of pi) with the 37th C. hexagon of 3997 and star 7993 with twin triangles of 5995. And the same centered hexagon (397) features just as prominently in the double anomaly in pi of the 70th star.

THAT.... in case you're wondering, is a mathematical signature, a signature composed of a specific arithmetic and a mirrored rearrangement of numbers (3's & 7's), now writ large in all the final three digits of every Fibonacci Number in existence; repeating infinitely a pattern in the most important number series in mathematics and science that is positively impregnated with obvious and plentiful Christian symbolism. In case you were wondering... .

And because the Fibonacci-1500 sum is a multiple of 1,000 (10x10x10) these patterns are also geometrically reversible:

The Fibonacci-1500 can alternate as a giant series of cube frames made of giant cubes, or a collection of 1,000 cube frame series.

'Cross'-Over Mechanics of the Golden Ratio

The Fibonacci family of numbers and related mathematics are one of the stars of science, which can be easily seen by two tell-tale signs seen in their listing on the OEIS scientific database: Namely it's low ID number A000045 (meaning it is only the 45th number series out of currently over 300k) and the length of the associated comments and cross-references. And this all for good reason, because the Golden Ratio is ubiquitous in the architecture of the universe (Google it) and the Fibonacci/Lucas Numbers are endlessly fascinating, so much so, that they have their own periodical.

One of the well-known nuggets of biblical mathematics (known to most researchers) is the fact that the first 60 decimals of phi (the Golden Ratio 1.6180339...) sums to 294, the ordinal Greek sum of one of the great primary names and identities of the discipline — Lord Jesus Christ. A good way to determine how important this is, is to run a search in the search bar above on that number and see how many items turn up, on mine or Leo Tavares's Mathematical Monotheism site.

The above graphic displays that this 'nugget' is more than coincidence, but encoded (or decoded) in a bewildering number of ways. The pertinent questions (mathematically) is whether or not there is a connection between the decimal expansion of phi and the repeat cycles of the Fibonacci Numbers. BECAUSE the first Fibonacci cycle is exactly 60 digits long!

Looking then to the next cycle, whose sum is the auspicious 14,800 (Christ x 10) we find that the decimal expansion of phi appearing to double down on the contention.

Click to ENLARGE

The plus sign configuration (112 x 16) is modular with the 2368 unilateral cross. 1792, being the 16th multiple of 112, is all to perfect, in that 1.6 is the closest 2 digit approximation of the Golden Ratio and that 112 is the original Hebrew for the Lord God (Yahweh Elohim) the full name of God. The fact that the Lord God sum fills out the Star of David, while the Jesus Christ sum fills only one of the two triangles may be of some theological importance.

This sort of figurative geometry agreement is one of the cornerstones of biblical mathematics. The above is one of its great flourishes. So what can we take from this bright flashing neon light at the crossroads of the Golden Ratio, the Fibonacci Numbers and biblical mathematics?

Obviously the name and number of the name Jesus Christ in Greek (2368) was specifically chosen for a great host of connections across the vast planes of math and science. We also see the basic principle of the star pattern of Genesis 1:1 writ large in these same domains. But we can also see that the 3D configurations of the sacred name are in no way incidental.

The cross cube 2368 (see the Jesus Cube) the unilateral cross shape connects in two ways with both geometries. The first creates a standing triangle of the 37 x 400 star and the second fills out the star by eliminating the unilateral dimensionality, i.e. it turns the cross in every direction into a cross of one dimension. The other cubes of 2368 display equal agreement with the great star of 14,800.

This sort of platforming (where the base 20x20) perfectly fits the adjoining geometry is proof positive, to say the least, of the design mechanic of biblical math(s). And if it doesn't prove the concept in the same way to you, all that means is that you have become immune to logic and evidence. Good luck with that!

In BLUE the dimensions of the New Jerusalem (12 x 12 x 12)

Please note: Most Bibles and commentaries on the book of Revelation and the New Jerusalem, almost always emphasize the WRONG thing. The commentaries quibble about the exact physical scale of an obviously spiritualized architecture; assuming that John in his Divine Vision, was seeing a physical object that could be measured in the hopelessly outdated and meaningless measure of the helplessly primitive metrics of the Greco-Roman world, like the length measurement of stadia. Clearly, in the context of a 1st Century Jew, who was a member of 12 Israelite tribes AND ALSO one of the 12 Disciples, it is the number 12 here that is the important feature!

To the average Christian, one of the most stunning features of the mathematics of the name Jesus Christ, is how it endlessly interacts with the dimensions of the New Jerusalem as described in the book of Revelation. The above graphic show the two known ways in which the math cooperates. The name and number (2368) forms a double layers cocoon around the 12th cube as as cubes are modular this pattern will tessellate infinitely. The unilateral cross cube formation will do this as well now surrounding each cube with 8 cross cubes.

The Jubilee Cross

The Fibonacci/Lucas cycles give rise to one of the most astonishing patterns yet seen in biblical mathematics, seen above as the Jubilee Cross an absolute concentration of the names sacred to Christianity. It is found in the strange and newly uncovered mechanics of the Fibonacci and Lucas cycles.

Above: the 3D combined walk of the first Fibonacci-Equalized-Lucas cycle, displaying their intrinsic modularity.

Of the various repeat cycles native to the Fibonacci Numbers, one stands out more than other in the discipline of biblical mathematics. This being the second cycle, the double digit Fibonacci-300. From a biblical math(s) perspective (based upon the preeminence of the patterns of Genesis 1:1) the number 300 has a very specific and theologically important identity, namely Ruach Elohim, the The Spirit of God, i.e. the Holy Spirit to the Christian, seen in the very next verse Genesis 1:2.

Genesis 1:2

And the earth was without form, and void; and darkness was upon the face of the deep.

And the Spirit of God moved upon the face of the waters.

It is the sum of this repeat cycle that is of immediate interest with its tell-tale number of 14,800; ten times that of Christ (1480) and one-hundred times that of the Hebrew Passover (148) Pesach. This Fibonacci sum of 14,800 is particular convincing, when we analyze it's ratio to the equivalent Lucas sum cycle. Here we see the same ratio (the original word for ratio in Greek was Logos) that we see in the Divine Name: Jesus & Christ (888 & 1480).

Fibonacci-300 cycle sum = 14,800

Lucas-60 cycle sum = 2500

14,800/2500 = 5.92

1480 - 888 = 592

Fibonacci-300 cycle sum = 14,800

Lucas-60 cycle sum (Equalized (x5)) = 12,500

14,800/12,500 = 1.184

2368/2 = 1184

592 x 2 = 1184

The double digit cycle itself is embedded with multiple math(s) which can be seen in the form of a matrix, most typically in columns of 12, the number 12 and 5 being the operative numbers of the cycles. Cycle 60 = 12 x 5, Cycle 300 = 12 x 5^2, Cycle 1500 = 12 x 5^3... .

There are multiple new-to-mathematics embedded geometries in these cycles. The tetrahedron shell (surface points) is a common feature to these cycles and is explored in depth (here in the Fibonacci Sequence page).

The number 7400 is also indicated in the columnar matrix and is an important geometry in its own right. This octagonal number pattern (explored at length in Star Math(s)) is also highlighted in the decimal expansion of pi and intimately related to the identities of the Sacred Name, here in English 925 and English ordinal 74.

This configuration can be dissected into the sacred name in English.

The Lucas Numbers share this pattern in their equivalent double digit cycle. The cycles of the Lucas Numbers, the mathematical twin of the Fibonacci Numbers, are modular and can only be understood together when they are equalized. The Lucas cycles, naturally, are 1/5 the length of all Fibonacci cycles.

By cycling the Lucas-60, fifty times, we create a cube (50^3). This cube, is the same cube indicated by the number 7400, the 50th octagonal number and the cubic spine of that cube. By extracting the six tetrahedral sides of the cube, we find an astonishing connection to the math(s) and identities of biblical mathematics.

This upright cross of 294, should be entitled The Jubilee Cross (of Christ), because it is composed of six of the 7th square (49). The Old Testament Jubilee, was celebrated every fifty years to honor the passing of every 7 x 7 years. Jubilee's were also celebrated in early American history and are noted importantly in Michael Medved's book The American Miracle.

This Jubilee Cross contains more than one reference to correct Hebrew and Greek mathematical identities:

In a massive multiplicity:

This octagonal number pattern of the Fibonacci cycle is clearly indicated by the columnar matrix. The image below shows how the matrix reiterates the basic geometry of an octagonal number (what were formerly called 'star-numbers'). Triangular numbers are the basic building blocks of all polygonal numbers and all non-centered polygonal numbers follow the basic template of the octagonal star pattern, see again Star Math(s).

This highlighted octagonal star, is a Christian jubilation, where it is the double digit Lucas-60 (2500) surmounted by T(49)'s.

Work in Progress. Check back soon!

But smart people (like I know you are) should be able to make sense of it from just the images!