Secrets of the Great Pyramid by Peter Tompkins (416 pages, pb, $18.95) Harper & Row, 1978 ISBN 0-06-090631-6
Does the Great Pyramid really embody precise proportions? Does it connect to earth and astronomical measurements? The resounding answer is Yes to anyone willing to apply themselves to the data in this detailed book. Tompkins (who also wrote The Secret Life of Plants) traces the history of research and measurements of the Great Pyramid, including all the faulty efforts. Tompkins puts the reader in the position of having all the data and references to verify his presentation. The geodetic information is extraordinary. To understand the ancients, one must understand the critical importance of earth measures.
I Ancient Background
II Medieval Exploration
III Renaissance and Revival of Interest
IV The Age of Enlightenment
V Exploring with Chisel and Gunpowder
VI First Scientific Theories
VII First Confirmation of Scientific Theories
VIII First Refutation of Scientific Theories
IX Scientific Theory Developed
X A Theodolite for Surveyors
XI Almanac of the Ages
XII Astronomical Observatory
XIII Astronomical Temples of Egypt
XIV Geodetic and Geographic Landmark
XV The Golden Section
XVI Scientific Survey Gives Geographical Proof
XVII Decline of Ancient Knowledge
XVIII Who Built the Pyramid? When? And How?
XIX Why Were the Pyramid Passages Plugged? When? And How?
XX Temple of Secret Initiation
XXI More Secret Passages and Chambers
XXII Astrological Observatory
Appendix: Notes on the Relation of Ancient Measures to the Great Pyramid
From pp. 189, 190 on The Golden Section:
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. This fact was inherent in Jomard's conclusions, but got lost in the babble of cubits.
Each flat face of the Pyramid was designed to represent one curved quarter of the northern hemisphere, or spherical 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 angle gives the pi relation between height and base.
John Taylor intuitively suspected something of the sort, but was unable fully to formulate it.
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 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.* Phi, like pi, cannot be worked out arithmetically; but it can easily be obtained with nothing more than a compass and straightedge.
With the incorporation of the Golden Section, the Great Pyramid provides an effective system for translating spherical areas into flat ones.
* 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.