Pi: a source book. (English) Zbl 0876.11001

New York, NY: Springer. xix, 716 p. (1997).

This book contains reprints of 70 articles dealing with \(\pi\) in one way or another, together with three appendices on the early history of \(\pi\), a computational chronology and formulae involving \(\pi\). The earliest article is the Rhind papyrus (c. 1650 B.C.) and the most recent the paper by D. Bailey, P. Borwein, and S. Plouffe [Math. Comput. 66, 903–913 (1997)].
Some of the greatest mathematicians, from Archimedes onward, are represented here for work that has advanced our knowledge of \(\pi\) – its calculation to more and more places, its irrationality and transcendence, its approximability by rationals, as well as statistics that support its (unproved) normality. Recent work shows the impact of computers and the development of algorithms that give fast convergence. There are also a number of more elementary expository articles.
Interspersed are curiosities such as the attempt to get the Indiana State Legislature to fix \(\pi\) by statute (and, in effect, patent it, although it was the wrong value) and mnemonics for \(\pi\) in prose and verse.
The editors state that “Both professional and amateur mathematicians \(\dots\) can find in [this book] a source of instruction, study, and inspiration”. They most certainly can.

Reviewer: H.J.Godwin (Egham)

MSC:

11-00	General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to number theory
00B60	Collections of reprinted articles
01-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to history and biography
11-03	History of number theory
11-04	Software, source code, etc. for problems pertaining to number theory
11Y16	Number-theoretic algorithms; complexity
11J81	Transcendence (general theory)

Keywords:

early history of \(\pi\); formulae involving \(\pi\); irrationality; transcendence; approximability by rationals; normality