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The Book of Numbers [Hardcover]

John H. Conway , Richard Guy
4.9 out of 5 stars  See all reviews (9 customer reviews)
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Book Description

March 16 1998 038797993X 978-0387979939 1st Corrected ed. 1996. Corr. 2nd printing 1998
"...the great feature of the book is that anyone can read it without excessive head scratching...You'll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow." -IAN STEWART, NEW SCIENTIST
"...a delightful look at numbers and their roles in everything from language to flowers to the imagination." -SCIENCE NEWS
"...a fun and fascinating tour of numerical topics and concepts. It will have readers contemplating ideas they might never have thought were understandable or even possible." -WISCONSIN BOOKWATCH
"This popularization of number theory looks like another classic." -LIBRARY JOURNAL

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Product Description

From Amazon

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.

Inside This Book (Learn More)
First Sentence
Throughout history, number and numbers have had a tremendous influence on our culture and on our language. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews

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4.9 out of 5 stars
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Most helpful customer reviews
5.0 out of 5 stars Numbers used as toys March 27 2001
By Charles Ashbacher TOP 1000 REVIEWER
To these "guys", numbers are toys, where the price of possession is nothing but a little knowledge. It is truly astounding, even for veteran mathematicians such as myself, to see how many different sets of numbers there are. They all have a story behind them, and given the multiple uses for so most of them, there are many more yet to be written.
Presented in a unique and engaging style that one associates with the authors, the numbers come to life with descriptions that hold your interest and leave you wanting more. The level of demonstration is not extremely technical, being well within the range of anyone who has been exposed to the topics of precalculus. Figures are used extensively, giving a visual interpretation of several ways in which the numbers can be used. Many of the numbers covered in the book are named after the person most responsible for making it famous, an aspiration that most mathematicians would no doubt confess to. In some cases, I was previously unaware of the name assigned to the numbers.
When I am in the mood for some light reading in mathematics, my preferred form is some type of listing of the properties of numbers. In this case, I found several hours of enjoyment and recommend it to anyone with similar tastes.

Published in Journal of Recreational Mathematics, reprinted with permission.
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5.0 out of 5 stars Superb but dangerous Jan. 10 1997
By A Customer
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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5.0 out of 5 stars Delightful!!! Sept. 8 2000
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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4.0 out of 5 stars Fascinating Insights into the World of Numbers Sept. 7 1998
By A Customer
An interesting review of the world of numbers from a pair of respected mathematicians. I E-mailed John Conway a question related to the book and he responded! The book opens many doors to higher mathematics, particularly number theory, the queen of mathematics.
The historical review makes the book a good addition to public libraries and high school libraries.
I particularly liked the review of Gregory Numbers.
It will wake you up mathematically even with a background of high school mathematics.
Teachers should find it useful to augment ciriculums in high school and college math classes.
Richard Brown Research Director 1248 Institute Charleston, SC
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5.0 out of 5 stars Artful Numbers Aug. 29 2001
This book is excellent. I am not a mathematician; my Ph.D. is in a social science, but my interest in intellectual history made this book worth it for me. The reason that it seems a bit expensive is because the authors use color illustrations. These are really helpful and make the book more exciting. The book is essentially number theory for a lay person. All you need to have is high school level math in order to start enjoying this book, so don't be afraid. Conway and Guy present a fascinating look at what the human intellect can achieve in the realm of abstract thought. Number theory, and mathematics in general, can be mysterioius, artful, and exciting. Highly recommended.
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