Computing the Digits in *

expression écriteComputing the Digits in pi Carl D. Offner September 6, 2009 Contents 1 Why do we care? 2 2 Archimedes 5 3 A digression: means 9 4 Measures of convergence 13 4.1 The rate of convergence of Archimedes' algorithm . . . . . . . . . . . . . . . . . . . . 13 4.2 Quadratic convergence . . . . . . . . . . . . . .acceleration of series 19 6.1 euler upper bound on the radius of the universe upper bound on the distance computer science answer fraction of the triplets 313 approach square root numbers error computer