I do not know to what extent, or in precisely what ways, Sumerian/Babylonian and Egyptian trade contacts may have led to a mutual influence on each others use of geometry and arithmetic. The main point that I was making is that we have every right to assume a form of geometric tradition at play in Old Kingdom times which existed concurrently with, and had an influence upon, an arithmetic (ie, computational) tradition.
As I said, these are two separate areas of expertise which would have run in separate channels, but which would have at the same time "informed" each other. In other words, I see no contradiction in computational modalities utilizing a geometric modality (such as the 8/9ths x D squared for area) while also using stricly computational modalities at other times. I do not see the Egyptians as having been of an "either or" mind set, but rather a "both and". A very non-western logic. (Hornung calls it a "quantum" logic.)