by
Charles William Johnson
The numbers of the perfect right triangle in two distinctive
variations (3•4•5 and 5•12•13) appear to have served as a basis for
some of the designs in ancient artwork. Other authors have noted the
relationship of the 3•4•5 perfect right triangle, but we have
possibly not suspected the close relationship shared by the 5•12•13
perfect right triangles present in the sites of Giza and
Teotihuacan. Previous discussions in this series have shown how
the numbers of the perfect right triangles, along with numbers
concerning relations of equivalency to the power of three, may be
graphed and then identify the layout of the pyramidal sites
mentioned. Let us offer only a few examples of this before we
discuss the relevance of the 5•12•13 numbers to the cube.
TEOTIHUACAN: MATCHES IN DESIGN AND LAYOUT
Many distinct variations of the basic designs exist, and these graphs
may be related to their numbers to the cube. It is significant to
note that some of the relations of equivalency, such as 1³+6³+8³ =
9³ (729 = 729) also reflect the day/year/cycle counts of the ancient
reckoning system. The most obvious are in the numbers 216 and 512
correspondingly to the 6 and 8 integers of the relation. However,
the series 5•12•13 does not reflect an apparent relation of
equivalency, yet the numbers to the cube are significant, since
their sum reveals a number series that also relates to the ancient
reckoning system: 5³ + 12³ + 13³ = 4050 or 125 + 1728 + 2197 = 4050.
The initial observation concerns the doubling/halving of 4050: 4050,
8100, 16200, 32400, 64800, 129600, followed by the Platonic
Year 25920. In other words, the sum of the natural number to
the cube series pertaining to the 5•12•13 perfect right triangle
yields the
duplatio/mediatio series relating to the yearcount of the
precession.
Now, consider the relationship with the previous series of the 1•6•8•9
relation of equivalency. The sum of 729 when doubled/halved yields:
729, 1458, 2916, 5832, 11664, 23328..., etc. The difference between
the relational step 23328 and 25920 is 2592; again the fractal
referring to the Platonic Year. In other words, in a natural
manner the historically significant numbers relating to the
precession, such as the
Platonic numbers or the Great Year, derive in a
natural fashion from the numbers of the perfect right triangles. In
ancient Kemi it is well known that
1296000 was historically significant.
The fact that the 5•12•13 numbers relate to the layout of the elements
and structures at Giza and, the fact that these particular
numbers to the cube as computated, refer to the numbers of the
precession, would appear to be of great significance once again for
considering the basis of science (math) within the ancient artwork.
The relationship between the numbers of the ancient reckoning
systems around the world and the architectural designs and the
designs in the sculptures, somehow defies the concept of mere
coincidences. Each time we find a specific relationship between the
numbers and the artwork, we obtain the idea of a conscious design,
and not the presence of happenstance; which would suggest that all
of these coincidences simply mean that the ancient reckoners
happened to have made the right mistakes. They just happened to have
chosen numbers that relate to natural series of numbers, which in
turn happen to be the ones related to astronomical events.
Furthermore, they just happened to have built thousands of pyramidal
structures that reflect the logic of these numbers, never suspecting
a direct relationship existed among all of these elements. Somehow,
to us, all of this happenstance rings hollow. It would appear to be
the case that the ancient reckoners knew what they were doing. The
significance of the 4050 series becomes obvious in relation to other
counts.
Consider the following
cases among many:

4050 x 260 = 1053000
(1053000/2 = 526500).

Now, consider the
Maya companion number 1366560/5265 = 259.56 whereby, the
fractal 25,956 is said to have been the Maya number
for the precession.

Furthermore, 5265 x 260c =
1368900, whereby we must remember that the numbers 1•3•6•8•9 refer
to previously studied basic designs in relations of equivalency;
and, 1368900  1366560 = 2340 (2340, 4680, 9360, 18720; the fractal
for the Maya long count
1872000).

4050 x 360c = 145800/2 =
(145800, 72900; the numbers of the 1•6•8 series)

4050 x 365c = 1478250/2 =
(739125, 369562.5, 184781.25, 92390.625, 46195.3125, 23097.5625,
11548.82813, 5774.414063, 2887.207031, 1443.603516,
721.8017578,
360.9008789...)

4050 x 584c = 2365200/2 =
(1182600, 591300, 295650, 147825, 73912.5, 36956.25, 18478.125,
9239.0625, 4619.53125, 2309.765625, 1154.882813, 577.4414063,
288.7207031, 144.3603516, 72.18017578, 36.09008789....)
In one sweep, we see how
the Earth count (365c) relates to the Maya
count (360c) and the Venus count (584c) relates to those two
counts. And, if we divide the Venus number 2365200 by five:

2365200/5 = 473040, 94608,
18921.6, 3784.32, 756.864, then we obtain interesting
combinations of numbers, remembering that 756 reflects Giza
and 864 reflects twice the Consecration number 432. Other authors
have shown how 108864 is significant, whereby 756/108 = 7 (another
historically significant number of the ancient reckoning system).
Innumerable ways exist for
conceiving the 5•12•13 numbers. Even 5 x 12 x 13 = 780 becomes
relevant, a Mars count among the ancient Maya
(3 x 260c = 780). Even the square of the 5•12•13 numbers reflects the
historically significant 52c of the ancient Mesoamerican peoples: 5²
+ 12² + 13² = 338 (338, 676, 1352, 2704, whereby 2704 is 52².
The relationships among the historically significant numbers appear to
be endless, just as one would imagine a mathematical computational
system to perform. Consider the strangeness of the following
computation, which is common to the Maya companion numbers in
relation to the numbers of the basic designs:

729 x 46656 = 34012224/2 =
17006112, 8503056, 4251528, 2125764, (1062882  1366560 = 303678)
Now, halve 303678, 151839,
which is one less than another Maya
historically significant number: 151840.
And, what about the
Nineveh number, 1959552 (fractal); it is obviously related
since 756 x 2592 = 1959552: 1959552/ 4050 = 483.83, 241.92, 120.96,
60.48, 30.24, 15.12, 7.56..., etc.
From these few examples, there should be no doubt that the numbers
relating to the perfect right triangles, based on the series that
begin with 3•4•5 and 5•12•13 relate easily to the historically
significant numbers of the ancient reckoning system when considered
from the cube of these numbers and in the form of rightangles
graphed designs. These basic designs obtained from graphing the
corresponding numbers of the perfect right triangles produce figures
that reveal a direct relationship to the layout of the pyramidal
structures at different sites around the world; especially at the
sites of Giza
and Teotihuacan.
Consider two additional
examples: 5121310.
From this relationship, it
would not be difficult to consider how the ancients may have walked
along the lines, thereby passing specific daycounts, yearcounts or
cyclecounts as reflected in the numbers. Between and among the
different structures, there would be a symbolization represented
that would reflect a particular count. The layout of the structures
follow, as far as we have been able to see, in almost every case one
of the basic designs based on the numbers of the perfect right
triangles, not only pertaining to the 3•4•5 perfect right triangle,
but to the less common 5•12•13 perfect right triangle series of
numbers. In fact, the side measurements of such a triangle, when
multiplied by 4, would reflect the integers 20³ + 48³ + 52³, and
reveal the sum of 259200, or ten Platonic Years (ten
precessional cycles).
These three integers reveal three historically significant number
series employed in the ancient reckoning systems of Mesoamerica
without a doubt: 20, 40, 80, 160, 320, 640, 1280, 2560, 5120,
10240...; 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576...;
and 52, 104, 208, 416, 832, 1664, 3328, 6656, 13312, 26624....
The numbers of the perfect right triangles form natural divisions
among the number counts and series. The historically significant
numbers relate and perform in accordance with the natural number
series coming out of the numbers corresponding to the different
perfect right triangles, and when taken to distinct powers, it would
appear that the historically significant numbers were chosen
precisely upon such a basis of reasoning. But, what is even more
intriguing is the fact that the events in nature, the astronomical
events such as the precession of the equinoxes (along with other
events at distinct levels of nature, such as the behavior of
electrons in the atom) also appear to reflect the different
numbers and number series coming out such relationships of
equivalency.
