Chris wrote:
"Although 362 cubits is more consistent with the surveys, it does seem an odd measure. One explanation is that the designers were using squares where the diagonal was more or less defined by a whole number. For example, a square with sides 362 cubits has to within a few centimeters, a 512 cubit diagonal. Interestingly the distance from the apex of the small subsidiary pyramid to the apex of the large pyramid is also 362 cubits."


Yes, what is at play here is but one example of what appears to have been a continuing interest not necessarily in Pythagorean Triples, but in what I refer to as Near Triples - such as the 99-99-140 which you cite. The 362-362-512 Triple notced by Legon is actually only one entry in a long sequence of extremely interesting Near Triples:

64-64-90.5
90.5-90.5-128
128-128-181
181-181-256
256-256-362
362-362-512
512-512-724

As I mentioned some time back in an earlier thread, there is no need to assume a knowledge of the Pythagorean Theorem, nor even knowledge that such a theorem might somehow exist. Both True and Near Triples (of relatively low length) are easily discoverable empirically - especially if you have an accurately delineated measuring rod and an ability to construct a right angle - both of which they had. Note that there is little way to distinguish between the True and Near Triples through empirical means - all that was perhaps seen at the time was that some Triples appeared to remain more accurate when doubled, tripled, etc. than did others.

The Near Triple phenomenon was perhaps even more important in the design of the Red Pyramid, but this is another story - although I must say it is a story which offers a rather stunning prediction which can be tested via a new survey to confirm the location of the center of the second chamber relative to the pyramid's north base edge. (As the horizontal passage and chamber lengths of the Red Pyramid are fairly well established, all that is actually needed is a precise confirmation of the location of the lower endpoint of the descending passage relative to the north base edge. The Perring and Dorner surveys are each problematic in this regard.)

Best,

Lee Cooper


PS - Infromation?