Vieta's famous product using factors that are nested radicals is the oldest infinite product as well as the first non-iterative method for finding [pi]. In this paper a simple geometric construction intimately related to this product is described. The construction provides the same approximations to [pi] as are given by partial products from Vieta's formula. Upper and lower bounds for the error are obtained in a visual way. (Contains 1 table and 1 figure.)