Re: Secrets of the Great Pyramid (Long)

Tue, 31 Oct 1995 14:22:23 EST

-- [ From: Luis G. Ordonez * EMC.Ver #2.10P ] --
Expanded recipient data:
cc: Francesco Balderacchi \ PRODIGY: (YPGQ04A)

>>In mathematics they were advanced enough to have discovered the
>>Fibonacci series, and the function of pi ...

> I believe that they thought that pi = 3.0.

> Greg Laden
> Department of Anthropology
> Harvard University
> 11 Divinity Avenue
> Cambridge MA 02138

"In the Great Pyramid the Egyptians produced a system of map
projection even more sophisticated than the one incorporated in the
ziggurats. The apex of the Pyramid corresponds to the pole, the
perimeter to the equator, both in proper scale. Each flat face of the
Pyramid was designed to represent one curved quarter of the northern
hemisphere, or sherical quadrant of 90 degrees.
To project a spherical quadrant onto a flat triangle correctly, the
arc, or base, of the quadrant must be the same length as the base of
the triangle, and both must have the same height. This happens to be
the case only with a cross section or meridian bisection of the Great
Pyramid, whose slope anle gives the pi relation between height and
The subtlety of the Pyramid's projection lies in the fact that when
viewed from the side, the laws of perspective reduce the actual area of
a face (mathematically oversized) to the correct size for the
projection, which is the Pyramid's cross section. What the viewer saw,
and sees, with the aid of perspective is the correct triangle. The key
to the geometrical and mathematical secret of the Pyramid, so long a
puzzle to mankind, was actually handed to Herodotus by the temple
priests (Heliopolis) when they informed him that the Pyramid was
designed in such a way that the area of each of its faces was equal to
the square of its height.
This interesting observation reveals that the Pyramid was designed to
incorporate not only the pi proportion but another and even more useful
constant proportion, known in the Renaissance as the Golden Section,
designated in modern times by the Greek letter phi, or 1.618. (If the
356 cubits of the Pyramid's apothem are divided by half the base, or
220 cubits, the result is 89/55, or 1.618.) Phi, like pi, cannot be
worked out arithmetically; but it can easily be obtained with nothing
more than a compass and a straightedge. With the incorporation of the
Golden Section, the Great Pyramid provides an effective system for
translating sperical areas into flat ones.
John Taylor set about drawing and redrawing every feature of the
Pyramid on the basis of the measurements reported by Howard-Vyse, so as
to see what geometrical or mathematical formulas might be derived from
the structure. Taylor was puzzled as to why the builders of the Pyramid
should have chosen the particular anle of 51 degrees 51' for the
Pyramid's faces instead of the regular equilateral triangle of 60
degrees. Analyzing Herodotus' report of what the Egyptian priest had
told him about the surface of each face of the Pyramid, Taylor
concluded they had been designed to be equal in area to the square of
the Pyramid's height. If so, this meant the building was of a
particular if not unique geometric construction; no other pyramid has
these proportions.
Taylor then discovered that if he divided the perimeter of the Pyramid
by twice its height, it gave hem a quotient of 3.144, remarkable close
to the value of pi, which is computed as 3.14159+. In other words, the
height of the Pyramid appeared to be in relation to the perimeter of
its base as the radius of a circle is to its circumference. This seemed
to Taylor far too extraordinary to attribute to chance, and he deduced
that the Pyramid might have been specifically intended by its builders
to incorporate the incommensurable value of pi. If so, this was a
demonstration of the advanced knowledge of the builders. Still today
the oldest known document which indicates that the Egyptians had a
knowledge of the value of pi is the Rhind Papyrus, dated about 1700
B.C., and therefore much later than the Pyramid. Found in the wrappings
of a mummy in 1855 by a young Scottish archeologist, Henry Alexander
Rhind, the rare papyrus is now in the British Museum. It gives a very
rough value for pi of 3.16.
Searching for a reason for such a pi proportion in the Pyramid, Taylor
concluded that the perimeter might have been intended to represent the
circumference of the earth at the equator while the height represented
the distance from the earth's center to the pole." (Which, with today's
technology, the Pyramid has recently been remeasured and computed in
1994 proving this to be true.)

Luis G. Ordonez