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Title: Mathematical Constants (Encyclopedia of Mathematics and Its Applications, Vol 94) by Steven R. Finch ISBN: 0-521-81805-2 Publisher: Cambridge University Press Pub. Date: 01 November, 2003 Format: Hardcover Volumes: 1 List Price(USD): $95.00

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Average Customer Rating: 5 (2 reviews)

Rating: 5
Summary: An essential component of all mathematical libraries
Comment: Until I read this book, I had no perspective on the number of significant constants there are in mathematics. Finch describes in complete detail a large number of constants of interest in mathematics, I didn't count how many are covered, but a list of one per line covers twenty four pages. It was also interesting to note that twelve of the pages list constants between zero and one. I couldn't help but wonder if this cluster represents a bias of the author or that mathematics is somehow naturally biased into this interval.
The coverage of each constant or group of constants follows the pattern of an explanation of how the constant arose, the formulas that are used to define it and an extensive set of references. So extensive that at times the paper devoted to the reference list rivals the amount spent in the explanation of the constant.
There are eight chapters, which group the constants into the following categories:

1) Well-known constants, which covers constants such as Ð, e and the golden mean.
2) Constants associated with number theory.
3) Constants associated with analytic inequalities.
4) Constants associated with the approximation of functions.
5) Constants associated with enumerating discrete structures.
6) Constants associated with functional iteration.
7) Constants associated with complex analysis.
8) Constants associated with geometry.

Separate subject and author indexes are in the back, a most sensible approach as many of the constants are named after the person who first described them.
I consider this book to be an essential component of all mathematical libraries. I have placed it on my "within the grasp" shelf and have strongly recommended to the college library that it be added to the reference collection.

Published in the recreational mathematics e-mail newsletter, reprinted with permission.

Rating: 5
Summary: An Instant Classic
Comment: This is an instant classic of mathematical exposition, a superb addition to the series Encyclopedia of Mathematics and Its Applications. Steven Finch's engaging style and lucid, self-contained essays on an amazing variety of topics will appeal to a wide audience. Beginners and experts alike will find a treasure trove of stories, unexpected appearances of numbers, connections between different subjects, and unsolved problems (e.g., if x is the square root of 2, is the tower of powers x^x^x irrational?).

From the Preface: "Material about well-known constants appears early and carefully, for the sake of readers without much mathematical background." The well-known constants include Pythagoras' square root of 2, the Golden Mean, Euler's e and gamma, Archimedes' pi, Apery's zeta(3), Catalan's G, Khintchine's K, Feigenbaum's delta, Madelung's M, and Chaitin's Omega.

There are chapters on constants associated with the fields of number theory, real and complex analysis, approximation of functions, enumeration of discrete structures (some from physics), functional iteration (e.g., paper folding), and geometry. A Table of Constants in decimal form directs the reader to sections of the book. Many sections have extensive lists of references, and Finch indicates exactly where in the literature one should look for rigorous proofs and further elaboration. Author and Subject Indexes complement each other. More than sixty figures illuminate the text.

This book shows the mysterious ubiquity and "unreasonable effectiveness" of certain universal constants. Anyone interested in mathematics will benefit from reading it.

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