The existence of a 3 x 4 rectangle as a design convention has been used repeatedly to suggest that the ancient Egyptians were aware of the Pythagorean Theorem.
The logical question is, is this a simple design convention employed by the Egyptians, or is it some kind of "occult encoding" of the 3-4-5 triangle (which is the only possible explanation for the repeated assertions that it is displaying their knowledge of same).
To examine this case, we would need to look at when and where the use of a 3 x 4 rectangle first appears in Egyptian mortuary structures, since it is these structures that are repeatedly used as "evidence" of the intentional occult encoding of the 3-4-5 triangle.
Bent Heick-Hansen, a researcher from Copenhagen, has done extensive research on the nature of certain design parameters and conventions with special attention to mortuary structures. In fact, it is his work that creates what is probably the most compelling argument linking the building of the Sphinx with Khufu, rather than Djedefre or Khafre. I will turn to his 1992 paper in Sesto Congresso Internazionale di Egittologia, Vol I, for his own words on this particular subject:
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In several instances, the drawings of groundplans of mastabas temples and temple complexes constructed during the Old Kingdom indicate that their interior layouts were divided into a 4:3 ratio. It is difficult to decide just why this particular ratio was found to be desirable and also to pinpoint when the concept arose... p. 243
So, he is in agreement that the 4:3 ratio was a common element. The discovery of the 3-4-5 triangle, however is another matter entirely. In the Archaic Period of Egypt, certain conventions, such as writing, were just being introduced. The evidence for the cubit (although possibly attributable to the body dimensions of Menes, first king of unified Kemet) is almost non-existant. The basic lifestyle was more hunter/gatherer than settled agrarian, although the existence of the two lands as a unified element was indeed a recent development. (Wilkinson and David both give excellent synopses of this era in Egyptian history in their respective books).
However, having the social institutions in place to devote time and energy to advanced mathematical research was probably not on their list of achievements. Ergo, I will now give the rest of the quote listed above:
Quote
...It is difficult to decide just why this particular ratio was found to be desirable and also to pinpoint when the concept arose. But it was certainly in evidence as early as the First Dynasty. (emphasis added) p. 243
This design convention for burial edifices had been around for centuries before it was used (along with several other standardized features) in the Dynasty IV pyramids.
It is important that we look at this design convention as such, and not attribute false meanings to it. As Heick-Hansen goes on to state:
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It is certain that this proportion has been one of primary principles of both builders and architects for thousands of years. This proportion has also been used outside Egypt and, up to our era, it has been strictly observed in the design and construction of a great number of ecclesiastical buildings in Europe. p. 243-244
I don't think anyone is going to make the argument that the 4:3 ratio was employed in European churches to clandestinely communicate the builders' awareness of the Pythagorean Theorem. To then do so to the Egyptians would be a serious double-standard.
So, if those who wish to state that the Egyptians of Dynasty IV were aware of the Pythagoran Theorum and were intent upon secretly encoding it in the burial edifices of their kings, then they are going to have to back themselves up to the First Dynasty to explain how and why those people did it for their kings... and non-kings as well.
Anthony
You can lead a horse to water but you can't make him think.
