The mystery surrounding the Great Pyramid has spawned a number of stories which seem plausible by today's standards, but which are clearly false if one takes into account the approximation to p used by the Ancient Egyptians themselves. One story concerning the Great Pyramid is that the perimeter of its base was constructed to be exactly equal to the circumference of a circle with radius equal to the height of the pyramid. The pyramid was 440 ells wide, and 280 ells high. This yields a required ratio of perimeter to diameter of 22/7, a commonly used approximation for p. Unfortunately this is common today, and is noticeably different from the approximation used at the time.

Problem 48 of the Rhind Papyrus suggests how the Egyptians may have obtained their method for finding the area of a circle. Consider the octagon obtained from a square of side 9 units by trisecting its sides and removing the four triangular corners. The area of the octagon seems to be differ little from that of the area of the circle inscribed in the square. The area of the octagon is easily calculated to be 63 square units, or roughly the area of a square of side 8 units.