This site provides a new, and perhaps for some a controversial, explanation for the rationale behind the exterior and interior design parameters of the Great Pyramid of Giza. Learn here: 1) the historical significance of the "golden ratio" and of the equal-sided pentagon (and pentagram); 2) a new theory for the derivation of the ancient Egyptian Royal Cubit; 3) a diagrammatic method by which the square root of any number can be derived; 4) how to diagrammatically derive a trigonometric table; 5) a relatively easy to follow presentation of Euclid's derivation of the 36 angle; 6) and now a newly added section detailing the derivation diagrams for the interior design parameters of the Red, Bent, Khafre, and Great Pyramids.

Introduction

As one delves into the exterior design details of the Great Pyramid, two striking numerical correlations emerge from the data, and these compel the serious student to either explain them as being nothing more than odd coincidence or to deal with their obvious implications. These findings are: First, that the pyramid's cross-section, as defined by its slant height (= 611.5 feet) divided by one half the length of a side (= 377.9 feet), embodies a numerical finding equal to the enigmatic ratio popularly known as the "golden ratio" (for a schematic of this situation refer to triangle ABC in Diagram 18 in the Pyramid section); and Second, that twice the perimeter of the Great Pyramid (that is, 377.9 x 16 = 6,046 feet) is a length that is precisely equal to the length of a minute of latitude as measured at the Earth's equator.

There appears to be no dispute regarding the reality of the above two pyramid lengths, as they have been determined by modern day survey. Rather, disagreement arises over whether or not the ancient Egyptians had a means by which they could produce the constant known today as the golden ratio, and whether or not they had developed the capability to measure the size of the Earth (and present their findings in degree measurement, no less). In other words, did they intentionally build the above knowledge into this pyramid, or do these numbers merely appear as a result of chance?

For the most part, archaeologists and historians assert that the existence of these relationships must be due to coincidence. The reasoning is that there is no incontrovertible proof to support intentionalism behind either numerical correlation. Still, there are some who consider this dismissal to be too abrupt, and who feel that the known surviving evidence is both too suggestive and too limited to preclude the possibility that the ancient Egyptians had gained certain awarenesses which were otherwise apparently ahead of their time. Although there has not been found a "smoking gun" to provide a universally accepted level of proof to support intentionality for the correlations mentioned, I believe it fair to say that there is likewise at present no conclusive evidence that the ancient Egyptians could not have found a way (such as is outlined in this essay) to achieve these results.

This issue of intentionalism is a question that continues to hold fascination, in no small part due to the specificity of the two numerical correlations mentioned here. In the process of becoming familiar with the design parameters of this pyramid, therefore, one can be excused for probing about for a cohesive and rational explanation, other than chance, that would account for these findings. As I began my own explorations into this situation it became evident that much could be gleaned by approaching the material from a position of devil's advocate - that is, starting from the assumption that the Egyptians of Old Kingdom Egypt had, in fact, intentionally built into the Great Pyramid the knowledge in question. With this as a point of beginning, entryways into the problem can then be established by focusing on two fronts: 1) How would it have been possible for the ancient Egyptians to have been able to arrive at these understandings using only the tools and advancements they are known, or can reasonably be inferred, to have had? and 2) With the architects having achieved these awarenesses, why would they then have designed the pyramid to incorporate this information? 

What follows in these pages is first an outline, and then a development, of the conclusions I have reached, with footnoted references to material providing greater depth and documentation. What I have derived, although admittedly not without some intracacy, is, I believe, logically consistent within the context of Old Kingdom capabilities, and within the realm of credible possibility. I have tried to present the ensuing discussions and diagrams as clearly and as directly as my abilities would allow, and I trust that those with an interest in the topic will persevere if and where necessary. The theories herein presented are speculative, and should be seen as such by the reader. My only claim is that these pages present a provocative and contextually consistent explanation for the stated Great Pyramid design realities, and perhaps for other related Old Kingdom design choices as well.

The core of this presentation proposes that the most compelling explanation for the intentional appearance of both the golden ratio, and of the length of a minute of latitude, in the design of the Great Pyramid is that Old Kingdom researchers had gained the ability to derive a fairly complete knowledge of trigonometric relationships some 2,000 years prior to the currently recognized date for said development by the ancient Greeks. Such an Old Kingdom accomplishment would likely have been achieved via the empirical exploration of geometric diagrammatic relationships in general, and the insights made available by the inscribed pentagon, in particular. Furthermore, with an aptitude for careful work and a trigonometric capability, shadow lengths could then have been used to determine the size of the Earth (as indeed they were by the later Greeks). Having attained the knowledge I describe, it is credible to reason that it was then held restrictively secret at the highest priestly levels in ancient times for reasons concerned with the centralization of power.

Since the relationship termed the 'golden ratio' is central to the diagrammatic derivation of the inscribed pentagon (and thereby to a continuum of trigonometric relationships), it is perhaps for this reason that it would have figured prominently in a building that was being designed to incorporate a primary unit of Earth measurement.

As is quite clear, the above summarization is meant only as a thumbnail sketch. The various aspects of the problem, in depth explanations, and much relevant documentation, form the remainder of this report. Tying into the integral context of the theory is also a discussion of a possible rationale behind the ancient Egyptians' choice of a length equal to 20.63 inches (= .524m) to be the length of their standard unit of measurement, the Royal Cubit.

 

Next: The Circle and the Square