The Book of Numbers Hardcover – 16 Mar 1998
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From the reviews:
"This is a really fascinating book either to read or to browse in, or for reference - there is a good index, and I can strongly recommend it - it should be in every school and college library!" The Mathematical Gazette
"… A delightful look at numbers and their roles in everything from language to flowers to the imagination." Science News
"… 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." New Scientist
From the Back Cover
In The Book of Numbers, two famous mathematicians fascinated by beautiful and intriguing number patterns share their insights and discoveries with each other and with readers. John Conway is the showman, master of mathematical games and flamboyant presentations; Richard Guy is the encyclopedist, always on top of problems waiting to be solved. Together they show us why patterns and properties of numbers have captivated mathematicians and non-mathematicians alike for centuries. The Book of Numbers features Conway and Guy's favorite stories about all the kinds of numbers any of us is likely to encounter, and many others besides. "Our aim", the authors write, "is to bring to the inquisitive reader...an explanation of the many ways the word 'number' is used". They explore patterns that emerge in arithmetic, algebra, and geometry, describe these patterns' relevance both inside and outside mathematics, and introduce the strange worlds of complex, transcendental, and surreal numbers. This unique book brings together facts, pictures and stories about numbers in a way that no one but an extraordinarily talented pair of mathematicians and writers could do.See all Product description
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There are few books on the market that cover this range of material at this level. There is little of the "gee whizz" that makes much of the popular literature so frustrating if you wish to go further but neither is it academic in its approach.
I found the book very readable. It's also well illustrated and produced. Although it does go into some quite deep areas you can start any chapter quite easily and move on if you find your head starting to spin. Unlike some popular science books, this is the real stuff and it will repay the time spent understanding it.
Most helpful customer reviews on Amazon.com
After the first two or three chapters, the book does seem rushed and there is much that I could not follow. I was especially frustrated by the method used to count the number of regions determined by the diagonals of a polynomial. It looks like a simple and original treatment of a classical problem, but after several attempts I just can't follow the logic.
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.