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.
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