In celebration of Pi Day 2024, I would like to explain how the “Arithmetic-Geometric Mean” of Gauss and Legendre can be used to give a rapid method for computing the digits of . By “rapid” here, I mean that the algorithm exhibits quadratic convergence: the number of correct digits roughly doubles with each iteration. I will mainly follow the exposition in Donald J. Newman’s 1985 paper “A Simplified Version of the Fast Algorithms of Brent and Salamin”.