Hi Mark,

Thanks, but unfortunately, I am still unable to visualize the connection of the mathematical assessments attributed to the Ancient Egyptians in your posts. Mainly because there is no archival proof they employed anything other than the area circle calculation noted in the papyri. There is no problem where they did not use the (8/9 d)^2 formula some form of problem #50 Rhind Mathematical Papyrus for circular calculations or the slightly different method noted in problem #10 of the Moscow Mathematical Papyrus to find the surface area of a hemisphere. What could explain this misconception is a long standing assumption that our concepts, principles and elements are somehow compatible with those employed by the Ancient Egyptians, When there is ample evidence showing two systems are not compatible.

Did the Egyptians really know pi? After all any value of pi is a value we have assigned and really based on an extrapolated figure from a single process of (8/9 d)^2 in problem #50 of the Rhind Mathematical Papyrus and is not a fact they knew pi, but an assumption on our part.
If you think about it a knowledge of pi is the one requirement necessary to make the extrapolation of pi in the form of 256/81 from (8/9 d)^2. Much less 22/7 or any other value of pi unless one considers the 5 1/2 seked.

Regards,
Jacob