Pi: The Next Generation

This book contains compendium§of 25 papers published since the 1970s dealing with p 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 brief key word list§indicating how the content relates to others in the collection. The collection§includes articles on actual computations of pi, articles on mathematical§questions related to p§(e.g., "Is pi normal?"), articles presenting new and often amazing techniques§for computing digits of p§(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 p, and articles presenting§new, high-tech techniques for analyzing p (i.e., new graphical techniques that permit one to§visually see if p§and other numbers are "normal").§§This volume is a companion to Pi: A Source Book whose third edition§released in 2004. The present collection§begins with 2 papers from 1976, published by Eugene Salamin and Richard Brent,§which describe "quadratically convergent" algorithms for p and other basic mathematical§functions, derived from some mathematical work of Gauss. The Bailey and§Borwein hold that these two papers constitute the beginning of the modern era§of computational mathematics. This time period (1970s) also corresponds§with the introduction of high-performance computer systems (supercomputers),§which since that time have increased relentlessly in power, by approximately a§factor of 100,000,000, advancing roughly at the same rate as Moore's Law of§semiconductor technology. This book may be of interest to a wide range of mathematical§readers; some articles cover more advanced research questions suitable for active§researchers in the field, but several are highly accessible to§undergraduate mathematics students.§§