Ronald wrote:

"I see the AE mainly as intuïtive builders, not as builders regularly using maths."


Up to this time my investigations have focused solely on the Khufu, Khafre, Bent and Red pyramids, but in all of these I have found that the design of each interior layout appears to be based on a squaring of the circle mechanism. The method used in every case is a relatively simple diagrammatic one, with the choices for the various alignments then taken from the diagram.

Some "fine tuning" appears to also have been a part of the process so as to either accommodate precise royal cubit intervals, or to accomodate a specific (and nearby) height to base ratio. In this way, the as-built construction could (in their minds) simultaneously satisfy more than one objective. The design methodology which I have proposed is, I believe, consistent with the mind set that we see in play in their approach to computational mathematics. A "break it up into a lot of little steps" approach, rather than what we would think of as a smoothly elegant one. This is not to disparage the Egyptian computational methods in any way. They were able to accurately produce the answers they needed to the problems which they encountered.

Also, the diagrammatic method which I have proposed to have been used in the pyramid interior design included either one or two shifts made to well defined segments of the diagram prior to construction. This "shift" mechanism was apparently an integral part of the design process, and I have speculated that it was used to either incorporate more aspects of the diagram, or to make it harder for anyone who worked on a part of the building to be able to correctly extrapolate their partial knowledge into the plan entire, or both.

So, I would say that what we might term "diagrammatic math" was most definitely employed in order to arrive at the height to base ratio of each pyramid's exterior, and the specific layout of each pyramid's interior. The correlations being aimed for were all based on relationships which we would recognize as being of a mathematical nature, be it to achieve a symbolic squaring of the circle resonance, a specific royal cubit dimension, or a specific height to base ratio. (Although they may not have been aware of the Pythagorean Theorem as such, one must understand that they could still have been very much aware of certain relationships which we would today recognize as being "Pythagorean" or "Pythagorean-like".)

My guess is that almost every aspect of their collective cultural creativity was, in one way or another, governed by "math", and perhaps by the very same principles seen in the pyramid designs. There is much written on their measurement systems - both linear and capacity, there is much written on their systems of proportion used in their graphic art, and there is much written on proportions seen in their non-pyramid buildings.

To quote from a cartoon I have on my wall, "At the risk of being both repetitive and redundant, let me say again" that the people who were the cultural architects and builders of the period were extremely competent and sophisticated. They were highly intelligent, and had a well considered why and wherefore behind their actions. I do not believe that the design and construction of the OK pyramids to have been anything remotely resembling a haphazard affair.

Best,

Lee Cooper