Of course Egyptians had an idea of numbers beyond the rationals. But all their scribes stopped at trying to find better approximations that were available stated in their chosen number domain, the rationals. Why else did pi's approximation stop at 256/81, possibly remaining at that level for over 1,000 years?
That is, my central point concerning belief, as Lee may have already read, can be summarized by:
**belief is a wonderful thing. In the case of Egyptian geometry, we'll all have to wait until direct evidence is presented that documents the use of irrational numbers or better approximations of pi, two subjects that exploded under the Greeks (and, of course, the irrational subject was not formally resolved until Gauss' 1796 use of complex numbers in the fundamental theorem of algebra). Yet, Egyptian arithmetic (stated in quotients and exact remainders) formed the basis of Greek arithmetic, and was not improved upon- in the manner that Greeks clearly improved Egyptian geometry by adding (improved) irrational number ( and pi approximation)s**