My interest in RMP # 48 lies more in what it tells us about AE involvement in exploring (and discovering) relationships through a diagrammatic approach. I believe that Problem 48 shows us not only a way to derive the area of a circle via its relationship to the area of its circumscribed square, but also a way to derive the circumference of a circle relative to the circumference (ie, perimeter) of this same circumscribed square.
That the Egyptians were extremely clever in their computational abilities within their chosen system is beyond argument. The terrain still to be proven is their similar level of aptitude within the realm of a simple, yet effective, form of diagrammatic geometry.
Perhaps your knowledge and insight into the computational thought processes of the AE scribe will allow you to see connections between their computational methodologies and the simple diagrammatic geometry of which I speak that are beyond the more obvious ones of which I am aware. Such insights would interest me greatly.