Did Egyptian scribes have an algorithmic means for determining the circumference of a circle? (Q643309)

On basis of problems in the Rhind and the Moscow Papyrus, particularly problem 10 in the Moscow Papyrus, the paper discusses two possible algorithms ancient Egyptian scribes had for determining the circumference of a circle. One, in essential the approximation of the circumference as \(22/7\) of the circle's diameter \(D\), is better known, and the second, suggested by the mentioned problem, reduces to \(256/81D\) by way calculating \((8/9)^2\) of \(4D\), the circumference of the square circumscribed to the circle (which is particularly interesting since it suggest a possible awareness that areas and circumferences of a square and its inscribed circle have the same ratio). Several related problems are discussed, as are architectural findings related to the need for a circumference-of-circle algorithm, and in the final part the author discusses possible reasons for having two different algorithms for the same purpose.