A Proposed Derivation Algorithm For
Ancient Egyptian Pyramid Design
The Red Pyramid -- The Bent Pyramid -- The Khafre (aka Chephren) Pyramid
The Khufu (aka Great) Pyramid
The essays made available here detail how the squaring of a circle in terms of its circumference, along with the squaring of a circle in terms of its area, can be used to provide an algorithm that allows one to derive the interior layout designs of the Red, Bent, Khafre, and Khufu pyramids - with results that with great consistency either exactly match, or are within one or two inches of, survey findings.
The methods used are all based on an empirically driven form of diagrammatic geometry. The relative measurements taken from the easily derived diagrams are presented along with the published survey information for each pyramid, and full references to these sources are given so that one may specifically evaluate all of the correlations provided by the diagrams.
Although the approach that is used in these derivations is quite simple, it will be shown that the architects' protocols apparently called for the inclusion of a unified "shift" factor in the original design diagram prior to each pyramid's construction. This may have been done in an attempt to keep the design's underlying knowledge restricted, as the implementation of a unified shift protocol introduces a simple - yet effective - trick of complexity to something that is otherwise fairly mundane. If the analyses given here are shown to be essentially correct, then it would certainly appear that it was this added step which has kept the interior design basis of these pyramids an enigma for so long.
The diagrams derived via the proposed conceptual approach explain why the pyramid architects chose to locate the various passageways and chambers of these pyramids where they did. In addition, these diagrams offer tantalizing insights into where might be found other interior pyramid features that have not as yet been discovered. In other words, the design algorithm lets one see what choices were available to the architects, and therefore which choices surveys tell us did indeed get used - and which choices still remained on the architect's drawing board as potential options. It is to be hoped that the findings and predictions given in these papers will be tested in the field in as timely a manner as possible.
The following essays address the four most well known and best preserved Egyptian pyramids of the Old Kingdom period:
The Khufu (aka Great) Pyramid Derivation Diagram - This derivation stems from the same two-fold squaring of the circle prerequisite seen in the other pyramids addressed here, but achieves this end in a somewhat more rigorous way. Although the level of sophistication may be of surprise, the resulting diagram accurately accounts for the positioning of almost all of the major interior features of this pyramid. As the proposed derivation presents a number of testable predictions, I believe time will eventually confirm that here we have the central theoretical basis for much of the interior design layout of this pyramid.
Among other things, this derivation explains the reason for, and the location of such curious aspects of this pyramid as: 1) the "Great Step"; 2) why the Grand Gallery is where it is, and why it ends where it does south of the pyramid's central axis; 3) why the descending entrance passage is located where it is, and why the ascending passage starts and stops where it does - and at the elevations that it does; 4) why the King's and Queen's Chambers are where they are; 5) why the walls of the King's Chamber extend down to the level that they do below the chamber floor; and 6) why the "doors" in the Queen's Chamber shafts are located where they are; and so on.
The Khafre (aka Chephren) Pyramid Derivation Diagram - This essay walks the reader through the methodology that was apparently used in plotting out the interior design layout of the Khafre Pyramid. Although the protocol follows fairly closely that seen in the Red and Bent Pyramid derivations, one is able to see that there was a willingness, if not an imperative, on the part of the architects to explore some simple variations on the basic design theme from one pyramid to the next. Among many other insights, this derivation explains the diagrammatic reasoning behind the existence and location of the mysterious internal connecting passage that was begun in this pyramid, but then blocked up and left unfinished, by the original builders.
Also explained is why there are two entrance passages to this pyramid, and why they are located where they are - and most notably, why one of these entrances is located on the ground outside of the pyramid itself.
The Red Pyramid Derivation Diagram - This essay shows how the basic 'two-fold squaring' methodology appears to very accurately account for the interior layout design of the Red Pyramid. Following this implementation, it is then shown how the slight steepening of the exterior sides from the initial "drafting table" design angle of 43°22' to an as-built angle of about 44°42' was accomodated. An accompanying essay (soon to be added) explores the possible reasoning behind the implementation of the slight increase in the Red Pyramid's exterior slope angle.
An unexpected finding of the derivation here proposed is that the center of the pyramid's second chamber would appear to be located some 4 feet to the north of where both the Perring and the Dorner survey reports have claimed it to be. This prediction offers a fairly straightforward mechanism by which the overall theory presented here may be put to the test.
The Bent Pyramid Derivation Diagram - Here we see the 'two-fold squaring' methodology providing a derivation explanation for the locations, elevations and slopes of both the north and west entrance passageways of this pyramid, along with an explanation for the locations of, and sizes of, the interior chambers. Also revealed is that the diagrammatic rationale for the location of the western entrance passage to this pyramid is a factor that exists in the other pyramid designs as well, and as such this feature may have been replicated, even if only in a symbolic fashion, in the interior constructions of the Red, Khafre, and Khufu pyramids.
There is every reason to presume that the methodology proposed in these derivations would also have been put to use in the planning of many of the other Old Kingdom pyramids, and perhaps also in the later period pyramids.
For anyone who is open to the possibility that the designs of these pyramids may have been conceived with a central theme in mind, I believe it will be well worth the time spent to delve into the simple geometry proposed in these essays. It is perhaps only by working through these results in a hands on manner that one can fully appreciate the simplicity, appropriateness, and accuracy of the method. I welcome, and in fact urge, that this theory be thoroughly put to the test.