Use a calculator (or program a computer) to calculate pi by iterating the algorithm of Archimedes given by lemma 1. How many iterations are necessary to get five decimal place accuracy? Lemma 1: Suppose OA is the radius of a circle and CA is the tangent to the circle at A. Let DO bisect angle COA and intersect the tangent at D. Then DA/OA=CA/(CO+OA) and DO2=OA2+DA2