"Wouldn't it be more fitting to offer geometric proofs in the Egyptian tradition, than in the Japanese ?" Perhaps, but what is the Egyptian tradition in such things ? Mathematics internationalized early on. From Ptolemaic times onward, Mathematics in Egypt is part of the Western Mathematical tradition, which traces its roots through Greece. In pre-classical times, the Egyptian mathematical texts that come down to us are descriptions of algorithms for the computation of areas, volumes, etc., devoid of anything resembling a proof. (Online commentary to the contrary, once the standard postmodernist buzz is removed, has merely illustrated the fact the commentators have no comprehension of what a mathematical proof is. The plugging of numbers into a formula doesn't count).

In ancient times, Algebra hadn't be developed yet, and Analytical Geometry (not developed until the time of Descartes) wouldn't have even been a possibility. If you wish to make an offering of this sort, that the ancients might have, if the thought had ever occured to them, Synthetic Geometry is the subject to look into. I recall that "College Geometry" by Altschiller and Court is a nice text in this area. (Sorry, no ISBN number, the book is too old. As time permits, I might start listing more recent, and more easily obtainable titles, but really, the best strategy is for you to drop by your local college library, and browse the Geometry portion of the Math section on your own).

Let us return, now.