The Book of Numbers (Hardcover)

~ John H. Conway (Author), Richard Guy (Author) "Throughout history, number and numbers have had a tremendous influence on our culture and on our language..." (more)
Key Phrases: tetrahedral number, frieze patterns, figurate numbers, New York, Martin Gardner, Neutral Hackenbush (more...)

Editorial Reviews

Amazon.com Review

The Book of Numbers lets readers of all levels of mathematical sophistication (or lack thereof) understand the origins, patterns, and interrelationships of different numbers. Whether it is a visualization of the Catalan numbers or an explanation of how the Fibonacci numbers occur in nature, there is something in here to delight everyone. The diagrams and pictures, many of which are in color, make this book particularly appealing and fun. A few of the discussions may be confusing to those who are not adept mathematicians; those who are may be irked that certain facts are mentioned without an accompanying proof. Nonetheless, The Book of Numbers will succeed in infecting any reader with an enthusiasm for numbers.

From Library Journal

The authors are well known to both academic and recreational mathematicians?Conway for inventing the "game of life" and discovering surreal numbers and Guy as the editor of the "Unsolved Problems" section in American Mathematical Monthly. They also coauthored the classic Winning Ways for Your Mathematical Plays (Academic, 1982). This popularization of number theory looks like another classic. Though number theory does not lend itself to fun and games, the authors take such joy in the order and patterns of numbers that you can't help being fascinated by what is actually a fairly difficult subject. A combination of clear verbal explanations, wonderfully clever diagrams, and equations (for the real mathematicians) make sometimes complicated numerical concepts accessible to those "without particular mathematical background" (i.e., who are not at least graduate students in mathematics). The material is simplified but not dumbed down. A bridge to understanding and appreciating higher mathematical concepts, this book could appeal to anyone from a mathematically sophisticated high school student to a university mathematics professor.?Amy Brunvand, Univ. of Utah Lib., Salt Lake City
Copyright 1996 Reed Business Information, Inc.

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Product Details

• Hardcover: 311 pages
• Publisher: Springer; Corrected edition (March 16, 1995)
• Language: English
• ISBN-10: 038797993X
• ISBN-13: 978-0387979939
• Product Dimensions: 9.4 x 6.3 x 1 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (16 customer reviews)
• Amazon.com Sales Rank: #350,367 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

16 of 16 people found the following review helpful:

4.0 out of 5 stars Gets off to a strong start, March 27, 2005

By	wiredweird "wiredweird" (Earth, or somewhere nearby) - See all my reviews (TOP 100 REVIEWER)

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Conway and Guy start this book with an enticing survey of how numbers pervade the English language, showing the hidden (or not-so-hidden) numerical roots of common words. They also mention other numbering systems, including the Roman numerals, Greek, Egyptian, and cuneiform Babylonian - numbers that persist in our 60-based measures of minutes and seconds, in both time and angle.

Next, they move into squares, triangular numbers, and many others with rich geometric meanings. Chapters 1 and 2, especially, create vivid images that bring many of their concepts to life. I had a bit of trouble finding ch.3's focus. It touches briefly combinatorics, a world in itself, and difference techniques. I found "Jackson's Fan" fascinating, but too terse for easy application to real problems. After this, the going gets a lot tougher, fast.

By ch 4, "Famous Families," the illustration is no longer as vivid as before. Ch. 6, on fractions and decimal expansions also held some interest - it touches on complexity in the decimal forms of fractions, and the numeric roots from which it springs. The section on continued fractions is only just enough to titillate without really enlightening. Discussion of imaginary numbers is OK, and offers some enjoyable insights. The section on quaternions, though, does a lot less to invite personal involvement and stir the imagination. Later sections of the book present readable surveys of their topics, but require a lot more form the reader in the way of determination and mathematical background.

If the whole book sustained the initial energy, it would have been an instant classic. The later parts of the book were clear, readable, and even enjoyable, but didn't match the breadth or vividness of the first half. I enjoyed this, but I may not come back to it.

//wiredweird

17 of 18 people found the following review helpful:

5.0 out of 5 stars Delightful!!!, September 8, 2000

By	James M. Cargal (Montgomery, AL USA) - See all my reviews (REAL NAME)

This is a delightful survey of numbers clearly aimed at as wide an audience as possible. However, as is always the case in such books the book is more formidable than it intends or than it looks. Still it is very friendly especially compared with, say, "Numbers" by Ebbinghays et al. The coverage is wide: primes, reals, Cayley numbers, Eisenstein numbers, polygonal numbers, catalan numbers, Stirling numbers of both types and of course Bell numbers. There are the cardinals and ordinals of Cantor as well as Conway's own surreal numbers. (And an earlier reviewer was correct about misprints and color problems.) I recommend this to anyone whose mathematical maturity is at least as great as basic calculus (and who is interested).

13 of 13 people found the following review helpful:

5.0 out of 5 stars Excellent, but not as good as ONAG or Winning Ways, November 17, 1999

By A Customer

Conway wrote On Numbers and Games. Conway, Guy, and Berlekamp wrote Winning Ways. These groundbreaking books are now hard to find. I hope both will be reprinted soon. The Book of Numbers has a short section on Combinatorial Game Theory -- just a taste. I expected much more about CGT. Still, TBON is an excellent book about numbers. Many diagrams, a lot of top-notch mathematics, and excellent writing fills each chapter. I would recommend this book for any high school student, but it would be quite enjoyable for fans of math at any level.