The essays made available here detail how the squaring of a circle in terms of its perimeter, and the squaring of a circle in terms of its area, can be used to provide what appear to be the original design rationales for the interior layouts of the Red, Bent, Khafre, and Khufu pyramids - usually to within inches of survey findings.

The methods used are all based on an empirically driven form of diagrammatic geometry. The relative measurements taken from the diagrams in the essays are presented in comparison with the published survey information for each pyramid, and full references to these sources are given so that one may specifically evaluate all claimed correlations.

Although the approach that is used for these derivations is quite basic, it will be shown that the architects' protocols 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 design basis of these pyramids hidden for so long.

Once one is aware of this conceptual approach - and its workings - the easily derived diagrams then provide remarkably accurate explanations as to how the various pyramid passageways and chambers came to be located where they are, and these diagrams also offer tantalizing insights into where might be found other features within these pyramids that have not as yet been discovered. As the potential rewards of the theory are truly great, it is to be hoped that the findings and predictions given in the papers below may be tested in the field by archaeologists sooner rather than later.

The following essays address the four most well known and most well-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 features of this pyramid. As this diagram presents a number of testable predictions, I believe time will eventually confirm that it is indeed the original theoretical basis for the interior design layout of this pyramid. Among other things, this derivation appears to have accurately predicted the location of the King's and Queen's Chamber "air shafts", and also the location of the so-called "doors" in the Queen's Chamber shafts. The diagram can then be used to predict the location of further possible, and as yet undiscovered, features in the Queen's Chamber shafts - and at other locations in the pyramid.

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 which is seen in the Red and Bent Pyramid derivations, one is able to see that there was a willingness, if not 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 existence and location of this pyramid's mysterious internal connecting passage that was begun, 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.

 The Red Pyramid Derivation Diagram - This essay shows how the basic 'two-fold squaring' methodology was apparently used to derive the interior layout design of the Red Pyramid. Following this implementation, it is then shown how the slight steepening of the exterior side from the initial "drafting table" design angle of 43°22' to an as-built design angle of about 44°42' was accomodated. An accompanying essay explores the reasoning behind why this slight increase in exterior slope angle may have been desired. Of surprise here is the finding that the center of the second chamber in this pyramid may be some 4 feet to the north of where the Perring and Dorner surveys have claimed it to be.

This prediction offers a fairly straightforward mechanism by which the overall theory may be put to the test.

The Bent Pyramid Derivation Diagram - Here we see the initiatory 'two-fold squaring' methodology in perhaps its purest form, and so providing a derivation rationale for both the north and west entrance passages of this pyramid. It is also pointed out how the mechanism for the design derivation of this pyramid's western entrance passage may have been replicated, even if only in a symbolic fashion, in the interior designs of the Red, Khafre, and Khufu pyramids detailed above.

There would appear to be little reason to doubt that the methodology used in the design of the four pyramids above would also have been employed in the designs of other Old Kingdom pyramids, and perhaps in the later period pyramids as well. I encourage others to pursue an analysis of these remaining structures along the lines detailed here.

For those who are interested in 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 your time to delve into the simple geometry that is proposed in these essays. It is perhaps only by checking 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.