A Rapidly Converging Recursive Approach to Pi

Although the general subject of the present arti cle has been treated in this journal frequently, the algorithm to be presented has not been discussed previously. THE ALGORITHM A geometric approach to the estimation of con sists of approximating a unit circle ever more close ly by a sequence of inscribed regular polygons of sides, each of length sn, and with circumference Cn and area An. For example, a sequence {nn} of values approximating can be obtained from