The following algorithm is based on work of Ramanujan and has been used in several world-record calculations of pi. Initialize a0 = 6 − 4 √2 and y0 = √2 − 1. Then compute and The terms an form a sequence of approximations to 1/π. The error in each approximation is given by This says that the number of correct digits roughly quadruples after each step. To see this, note that the number of correct d