
Re: Ariadne's thread
Posted:
Nov 25, 2011 2:52 AM


The Maya method of calculating the circle, perhaps encoded in the Venus Pyramid (Citadel), is based on the number 13 and the starting triple 51213. The Babylonian method, I believe, was based on the number 17 and the starting triple 81517. And the Egyptian method, encoded in the Great Pyramid, was based on the number 5 and the Sacred Triangle 345 or 152025 or 75100125 or 375500625 ... JeanPhilippe Lauer recognized this triangle in the socalled King's Chamber of the Great Pyramid: diagonal of a short wall 15 royal cubits, length of the chamber 20 royal cubits, diagonal of the volume 25 royal cubits.
Every subdivision of the radius, from 5 to 25 to 125 to 625 ... makes a new triple emerge, from 345 to 72425 to 44117125 to 336527625 ... If you know a triple and wish to find the next one, calculate these terms
+3a +4b / +3b +4a / 5c
and choose the positive values for the pair of long terms that are neither zero nor divisible by 5 (in the case of the Maya method you have to calculate the terms + 5a +12 b and +5b +12a and 13 c, and choose the positive values for the long terms that are neither zero nor divisible by 13).
The arms of the cross mark 4 points on the circle, the triples 8 and 8 and 8 and 8 ... more points. The resulting polygon has 12 20 28 36 ... sides of two or three different lengths (never more) that are whole number multiples of the square roots of 2 and/or 5 and/or 2x5 (2 and/or 13 and/or 2x13).
The square root of 2 is approximated by the number column whose first lines are 1 1 2 / 2 3 4 / 5 7 10 / 12 17 ..., and the square root of 5 by the number column whose first lines are 1 1 5 / 2 6 10 / 1 3 5 / 4 8 20 / 2 4 10 / 1 2 5 / 3 7 15 / 10 22 50 / 5 11 25 / 16 36 80 / 8 18 40 / 4 9 ...
The polygon inscribed in the circle of radius 25 and diameter 50 is defined by the triples 152025 and 72425. It has 20 sides of two different lengths, 12 sides of 5 times the square root of 2, and 8 sides of 4 times the square root of 5
12 x 5 x sqrt2 plus 8 x 4 x sqrt5
Considering that the circumference of the circle is a little longer than the periphery of the inscribed polygon we may choose values that are a little above the actual roots, 17/12 and 9/4
12 x 5 x 17/12 plus 8 x 4 x 9/4 equals 157
Divide the periphery 157 of the numerically rounded polygon by the diameter 50 and you get 157/50 = 3.14 for pi, from the sequence
3/1 (plus 22/7) 25/8 47/15 69/22 ... 157/50 ...
The base of the Great Pyramid measured 440 and the height 280 royal cubits. Imagine a circle whose vertical diameter is given by the height of the pyramid. Its area equals the one of the pyramid's crosssection (implicit pi value 22/7). As if the pyramid, symbol of the Primeval Hill, released the solar disc of Ra ...

