## Pi: The Next Generation: A Sourcebook on the Recent History of Pi and Its ComputationThis book contains a compendium of 25 papers published since the 1970s dealing with pi and associated topics of mathematics and computer science. The collection begins with a Foreword by Bruce Berndt. Each contribution is preceded by a brief summary of its content as well as a short key word list indicating how the content relates to others in the collection. The volume includes articles on actual computations of pi, articles on mathematical questions related to pi (e.g., “Is pi normal?”), articles presenting new and often amazing techniques for computing digits of pi (e.g., the “BBP” algorithm for pi, which permits one to compute an arbitrary binary digit of pi without needing to compute any of the digits that came before), papers presenting important fundamental mathematical results relating to pi, and papers presenting new, high-tech techniques for analyzing pi (i.e., new graphical techniques that permit one to visually see if pi and other numbers are “normal”). This volume is a companion to |

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### Contents

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3 The arithmeticgeometric mean of Gauss 1984 | 21 |

4 The arithmeticgeometric mean and fast computation of elementary functions 1984 | 79 |

5 A simplified version of the fast algorithms of Brent and Salamin 1985 | 97 |

6 Is pi normal? 1985 | 103 |

7 The computation of π to 29360000 decimal digits using Borweins quartically convergent algorithm 1988 | 108 |

8 Gauss Landen Ramanujan the arithmeticgeometric mean ellipses π and the Ladies Diary 1988 | 124 |

15 Similarities in irrationality proofs for π ln2 2 and 3 2001 | 229 |

16 Unbounded spigot algorithms for the digits of pi 2006 | 241 |

Plausible reasoning in the 21st Century 2008 | 254 |

18 Approximations to π derived from integrals with nonnegative integrands 2009 | 292 |

A survey 2009 | 301 |

20 The computation of previously inaccessible digits of π2 and Catalans constant 2013 | 324 |

21 Walking on real numbers 2013 | 340 |

22 Birth growth and computation of pi to ten trillion digits 2013 | 362 |

9 Vectorization of multipleprecision arithmetic program and 201326000 decimal digits of pi calculation 1988 | 150 |

10 Ramanujan and pi 1988 | 165 |

11 Ramanujan modular equations and approximations to pi or how to compute one billion digits of pi 1989 | 175 |

12 Pi Euler numbers and asymptotic expansions 1989 | 196 |

13 A spigot algorithm for the digits of π 1995 | 205 |

14 On the rapid computation of various polylogarithmic constants 1997 | 216 |