circle is just plain good luck. Obtaining a better approximation to the area using finer divisions of a square and a similar argument is not simple. Problem 50 of the RMP finds the area of a round field of diameter 9 khet. This is solved by using the approximation that circular field of diameter 9 has the same area as a square of side 8. Problem 52 finds the area of a trapezium with (apparently) equally slanting sides. The lengths of the parallel sides and the distance between them being the given numbers. Hemisphere: Problem 10 of the MMP computes the area of a hemisphere. Volumes Several problems compute the volume of cylindrical granaries (41, 42, and 43 of the RMP), while problem 60 RMP seems to concern a pillar or a cone instead of a pyramid. It is rather small and steep, with a seked (slope) of four palms (per cubit). A problem appearing in section IV.3 of the Lahun Mathematical Papyri computes the volume of a granary with a circular base. A similar problem and procedure can be found in the Rhind papyrus (problem 43). Several problems in the Moscow Mathematical Papyrus (problem 14) and in the Rhind Mathematical Papyrus (numbers 44, 45, 46) compute the volume of a rectangular granary. Problem 14 of the Moscow Mathematical Papyrus computes the volume of a truncated pyramid, also known as a frustum. Seked Problem 56 of the RMP indicates an understanding of the idea of geometric similarity. This problem discusses the ratio run/rise, also known as the seked. Such a formula would be needed for building pyramids. In the next problem (Problem 57), the height of a pyramid is calculated from the base length and the seked (Egyptian for slope), while problem 58 gives the length of the base and the height and uses these measurements to compute the seked. In Problem 59 part 1 computes the seked, while the second part may be a computation to check the answer: If you construct a pyramid with base side 12 [cubits] and with a seked of 5 palms 1 finger; what is its altitude? References Bibliography Egyptian mathematics History of geometry