2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156456In 1987 Jonathan and Peter Borwein, inspired by the works of Ramanujan, derived many efficient algorithms for computing $π$. We will see that by using only a formula of Gauss's and elementary algebra we are able to prove the correctness of two of them.To appear in The American Mathematical Monthly. (6 pages)Number TheoryClassical Analysis and ODEs33E05text