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Pi: The Next Generation

David H. Bailey and Jonathan M. Borwein
Publication Date: 
Number of Pages: 
[Reviewed by
Allen Stenger
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This book is a sequel to Berggren & Borwein & Borwein’s Pi: A Source Book. That book has grown through three editions, and has become unwieldy at 800 pages (the binding split on my copy), so rather than revising it again the authors have started a new volume with papers published from 1976 to 2015. There’s some overlap with the previous volume; I counted 12 papers (out of 25) in the new volume that also appear in the old volume.

As before, the book consists of reprints of the most important papers in the field. (Some of you may be surprised to hear that \(\pi\) is a field, but with several entire scholarly and popular books on it, I think it qualifies.) Most of the papers deal with calculating \(\pi\) to many digits of precision, dealing both with the computer implementation and with new algorithms. In the 1970s very fast parallel and vector computers were becoming available, and there are several papers with detailed studies of how these new architectures can be used to calculate \(\pi\).There are also a few papers on the question of whether \(\pi\) is a normal number (in other words, whether the digits are asymptotically equi-distributed), some surveys of \(\pi\) and its lore, and a few miscellaneous papers on the irrationality of \(\pi\) and on spigot algorithms (algorithms that produce the exact digits one at a time, rather than producing successively-better approximations and reading the digits from there).

The new book follows the same layout and selection criteria as its predecessor, so if you liked that one, you’ll like this one too. Very Good Feature: an extensive index (this is unusual for collections of papers).

One flaw of the new book is the table of contents: it only lists the paper titles, while the old book also listed the author and a one-sentence abstract. The production quality is poor in some instances. Some of the reproductions are poor quality: so poor that you can see the digitized pixels with the naked eye. Paper 2 is especially bad: it is both pixilated and fuzzy (but still readable). This is one of the papers that also appeared in the earlier volume, but the earlier reproduction was much higher quality. Extraneous material that appears at the end of a paper, such as advertisements, fillers, or the beginning of the next paper, are not blanked out as they usually are in collections.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His personal web page is His mathematical interests are number theory and classical analysis.

See the table of contents in the publisher's webpage.