I have been extremely busy of late (and still am!) so forgive my not having posted in a while.
Franz and Milo, both of you are offering tremendous insights here, insights worthy of much broader discussion and exploration. Franz, I share your belief that Egyptian capabilities are only hinted at in the surviving papyri, and I also share Milo's rejoining that speculation is but speculation - until explicit proof is found. I suppose "proof" can be in the eyes of the beholder, but in general I would say that a hypothesis can be proved if it provides predictions of as yet unknowns which can then be shown to be true.
This is precisely the point I have struggled with for the past few years. I am able to formulate testable predictions regarding the interiors of some of the Old Kingdom pyramids, but have not the wherewithal to perform, or cause to be performed, the explorations necessary.
Should these predictions ever be proved accurate, it would go a long way to showing how involved the Egyptians were in diagrammatic geometry and number, and in what directions they took their involvement.
Perhaps such geometric byways offer insight into their calculation byways, but although I have done some very preliminary work in this direction, I do not feel that I am quite adept enough to take it very far. This is, however, exactly why I am interested in RMP 48, in that it seems to me to lead to precisely this kind of bridge in regard to calculating a circle's circumference.
I continue to greatly appreciate and enjoy these discussions.. As to Mr. Hossam Aboulfotouh's post, I fear I am not qualified to offer any insights to his comments.