This 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 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 pi and other basic
mathematical functions, derived from some mathematical work of Gauss.
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.
