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    Pi Iterations

    Definition

    π may be computed using a number of iterative algorithms. The best known such algorithms are the Archimedes algorithm, which was derived by Pfaff in 1800, and the Brent-Salamin formula. Borwein et al. (1989) discuss pth-order iterative algorithms. The Brent-Salamin formula is a quadratically converging algorithm. Another quadratically converging algorithm (Borwein and Borwein 1987, pp.