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The Book of Numbers Corrected Edition

23 customer reviews
ISBN-13: 978-0387979939
ISBN-10: 038797993X
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Editorial Reviews 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: 310 pages
  • Publisher: Copernicus; Corrected edition (March 16, 1995)
  • Language: English
  • ISBN-10: 038797993X
  • ISBN-13: 978-0387979939
  • Product Dimensions: 9.2 x 6.3 x 0.9 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (23 customer reviews)
  • Amazon Best Sellers Rank: #232,036 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

38 of 39 people found the following review helpful By wiredweird HALL OF FAMETOP 1000 REVIEWER on March 27, 2005
Format: Hardcover Verified Purchase
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.

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27 of 28 people found the following review helpful By James M. Cargal on September 8, 2000
Format: Hardcover Verified Purchase
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).
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14 of 15 people found the following review helpful By R. Holmes on May 23, 2012
Format: Hardcover
I'm not sure why it took 17 years for me to catch up with John H. Conway and Richard Guy's The Book of Numbers. I don't even recall hearing about it until I came across it in a local library.

It is, I'm sorry to say, not as good as I'd hoped. They would have written a better book had they chosen about half as many topics, or written about twice as many pages. As it is, there's far too many steps left out, too much unexplained, too many terms undefined. To pick just one example, in the section "Lagrange's Numbers, Markov's Numbers, and Frieman's Number" in Chapter 7, the last paragraph is about the Lagrange spectrum, the Markov spectrum, and Frieman's number. One paragraph? It needed more. I would guess that people who already learned about these things once might read Conway and Guy's discussion, nod, and say, "Oh yes, I remember that." For me, who'd not encountered them before, the paragraph was opaque. There simply wasn't enough information conveyed to promote any understanding. Omitting that paragraph, or perhaps that entire section, would have been an improvement, if they didn't want to expand the discussion to a page or so.

There should have been better proofreading, as well. In the caption to Figure 10.8, to pick one of several problems I noticed, the fraction 6/14 should be 1/64.

It's a shame. Conway and Guy could have written a much better book had they not been in such a rush to get through so many subjects.
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18 of 20 people found the following review helpful By A Customer on November 17, 1999
Format: Hardcover
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.
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17 of 19 people found the following review helpful By A Customer on January 10, 1997
Format: Hardcover
A personal but fascinating review of numbers: from Egyptian
fractions to surreal numbers; from numbers so large they cannot
be imagined (and barely be named) to ruler-and-compass; all prefaced by
a virtuoso etymologic riff.

Beautifully produced, engagingly written, full of new perspectives
on old material - and new material too. The book contains so
much disparate information that each reader will find
something in particular that he or she likes. I do not
think I have ever seen a popularization at once so interesting
to anyone from bright junior high-school student to a professional

I have two minor complaints. First, there are some misprints
(for example in the description of trisections), and in some of
the early diagrams the orange and the red tiles come out looking
the same. In view of the extraordinary complexity of the
production and in view of the overall visual appeal and
clarity of the presentation, these slight errors do not
detract from the impact.

The more serious problem has to do with the fact that the
book is so fascinating
that it can be a real time sink. I have personally lost many
hours pondering the big (and I mean /big/) numbers Conway
and Guy describe, for instance. The book is almost like a
CD-ROM game in that one can get completely lost in it for days.
It made me wistful, too, that I had not had this book when I was first
learning mathematics (also, it could use a few more references
to things like Graham's number and surreal asymptotics).
Not only that but, despite its fairly hefty price tag, I
find myself buying copies for friends - so it can use up
not only a lot of time but money too!
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