Mathematical Constants (Encyclopedia of Mathematics and its Applications) [Hardcover]

Steven R. Finch (Author)

Book Description

Publication Date: August 18, 2003 | ISBN-10: 0521818052 | ISBN-13: 978-0521818056

Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

Editorial Reviews

Review

"Enormous fun, and you don't even have to follow any difficult arguments; a treasure-trove for the mathematical beachcomber."
The Mathematical Gazette

"I think all mathematicians should own this book...there are sections where the author conveys admirably his excitement over some unexpected and beautiful sequence of ideas. I pay the author the earnest compliment of stating that nearly every page in the book is an adventure."
The Mathematical Intelligencer

"Very accessible...The author's clear and engaging style makes the book a pleasure to read."
MAA Reviews

"This is a very useful book...The emphasis is on the mathematical origin of the constants and their interrelationships. The aim is always to be clear and complete, to motivate why a particular constant or idea is important, and to indicate exactly where in the literature one should look for rigorous proofs and further elaboration. This book should be in each mathematical library."
Monatshefte für Mathematik

"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."
Charles Ashbacher, amazon.com

Book Description

Here Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book will be helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This is an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

Product Details

• Hardcover: 624 pages
• Publisher: Cambridge University Press (August 18, 2003)
• Language: English
• ISBN-10: 0521818052
• ISBN-13: 978-0521818056
• Product Dimensions: 9.4 x 6.2 x 1.7 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #957,790 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

26 of 26 people found the following review helpful:

5.0 out of 5 stars An Instant Classic, September 29, 2003

By 

Jonathan Sondow (New York, NY) - See all my reviews

This review is from: Mathematical Constants (Encyclopedia of Mathematics and its Applications) (Hardcover)

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.

16 of 17 people found the following review helpful:

5.0 out of 5 stars An essential component of all mathematical libraries, October 19, 2003

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Mathematical Constants (Encyclopedia of Mathematics and its Applications) (Hardcover)

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.

2 of 3 people found the following review helpful:

5.0 out of 5 stars A beau book, October 26, 2007

By 

V. Rio (Lujan.Buenos Aires. Argentina) - See all my reviews
(REAL NAME)   

This review is from: Mathematical Constants (Encyclopedia of Mathematics and its Applications) (Hardcover)

I write bad in English. Then, my review is in languaje Spanish.

Yo pienso que este es un excelente libro. Lo compre por mi interés en teoría de números. Suponía que el libro trataría sobre muchas de las constantes en este campo de la matemática. Y asi es. Es toda una enciclopedia en constantes matemáticas con una abundante bibliografía refiriendo al lector a los papers originales. El trabajo del Profesor Finch es excelente. Un gran libro. Lo recomiendo a todo aquel que ama la matemática y ve algo bello en el numero pi, en el numero e, en la raíz cuadrada de 2, en la constante de Euler, etc.

Rafael Jakimczuk