Customer Reviews

The Book of Numbers

5 star:		(11)
4 star:		(6)
3 star:		(0)
2 star:		(1)
1 star:		(0)

 

 

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

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.

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).

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.

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 mathematician.

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!

This is an 'almost done' type of book. I like the way the subject is handled. The pictures and the thoughts that go with them are really good food for thought. Still, when I read the text, I get the feeling that this book was rushed to press. One more review by the author could have helped. I get this feeling because the text does not always follow the illustrations. It neither does much to elaborate on them or to completely discuss what has been included.

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.

I own a lot of books on Mathematics and Mathematical topics. This book truly is my favorite. The color illustrations, the other drawings and diagrams make the topics very understandable and tantalizing. The section on infinite and infinitesimal numbers alone, has inspired me to submit a paper on this subject to a Mathematics Journal. This book will cause anyone who is not already a Mathphile, to quikly become one. Take a look at the middle numbers in Pascals Triangle....with a little manipulation of this sequence, you produce CATALAN NUMBERS, which further leads to a number of interesting problems with Friezes and Polygons, none of which are mind bending in their demand of your mental powers. The chapters are all short, and you can open the book at random and find something very nice to dine on. BUY THIS ONE! Dr.Pratt.

The authors present novel and surprising results about different varieties of numbers, with enough elementary discussions to provide readers with a high school background their money's worth. Prime numbers, Fibonacci numbers, Catalan numbers, Fermat numbers, imaginary numbers, infinite numbers, games, counting, patterns, etc. are included. The range of material includes much that will appeal to the expert as well as the novice.

I enjoyed reading this book very much. But I do not agree with the reviewers who say it does not require more than a highschool level in mathematics.
I have an M.Sc. degree in electrical engineering, so I can safely say I have a good knowlegde of mathematics, but still there were parts I didn't completely understand.
Maybe we don't have to understand it all at once, maybe this level is needed to keep it interesting. And interesting it was, right up to the last page. And after reading the last page, I would have loved to read more like it.