From a very early date the Egyptians may well have been aware of the 3-4-5 relationship, and many other Triple and near Triple right-triangle relationships, without having any knowledge of the Pythagorean Theorem - nor with any inkling that such a theorem might even exist.

As I mentioned in another thread [www.hallofmaat.com] it is child's play to discover these relationships empirically. All that is needed is the ability to accurately create a right-angle, the ability to accurately subdivide linear measurement tools, a flat surface, and a careful procedural method. Once discovered, certain of these Triples and near Triples (and their multiples) could then have been seen as being of unique significance for a variety of reasons, reasons both symbolic and practical.

Note that without a knowledge of the Pythagorean Theorem there is then no definitive way to know that some of the Triples discovered empirically are "true" Triples, while others are merely "apparent", or "near", Triples. This means that many "apparent" Triples could have been seen as being just as valid (or useful), and in some cases perhaps even more valid (or useful), than a true Pythagorean Triple. My sense is that this may indeed have been the case in pyramid design.

Lee Cooper