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Re: Ariadne's thread
Posted:
Nov 25, 2011 2:52 AM
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The Maya method of calculating the circle, perhaps
encoded in the Venus Pyramid (Citadel), is based
on the number 13 and the starting triple 5-12-13.
The Babylonian method, I believe, was based on
the number 17 and the starting triple 8-15-17.
And the Egyptian method, encoded in the Great
Pyramid, was based on the number 5 and the
Sacred Triangle 3-4-5 or 15-20-25 or 75-100-125
or 375-500-625 ... Jean-Philippe Lauer recognized
this triangle in the so-called 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 3-4-5
to 7-24-25 to 44-117-125 to 336-527-625 ... 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 15-20-25
and 7-24-25. 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 cross-section
(implicit pi value 22/7). As if the pyramid, symbol of
the Primeval Hill, released the solar disc of Ra ...
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