Pi: The Next Generation: A Sourcebook on the Recent History of Pi and Its Computation

Foreword.- Preface.- Introduction.- Computation of pi using arithmetic-geometric mean.- Fast multiple-precision evaluation of elementary functions.- The arithmetic-geometric mean of Gauss.- The arithmetic-geometric mean and fast computation of elementary functions.- A simplified version of the fast algorithms of Brent and Salamin.- Is pi normal?.- The computation of pi to 29,360,000 decimal digits using Borweins' quartically convergent algorithm.- Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, pi, and the ladies diary.- Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of pi calculation.-Ramanujan and pi.- 11. Ramanujan, modular equations, and approximations to pi or how to compute one billion digits of pi.- Pi, Euler numbers, and asymptotic expansions.- A spigot algorithm for the digits of pi.- On the rapid computation of various polylogarithmic constants.- Similarities in irrationality proofs for pi, ln 2, zeta(2), and zeta(3).- Unbounded spigot algorithms for the digits of pi.- Mathematics by experiment: Plausible reasoning in the 21st century.- Approximations to pi derived from integrals with nonnegative integrands.- Ramanujan's series for 1/pi: A survey.- The computation of previously inaccessible digits of pi2 and Catalan's constant.- Walking on real numbers.- Birth, growth and computation of pi to ten trillion digits.- Pi day is upon us again and we still do not know if pi is normal.- The Life of pi.- I prefer pi: A brief mathematical history and anthology of articles in the American Mathematical Monthly.- Bibliography.- Index.