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The Book of Numbers ReviewConway 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.
//wiredweirdThe Book of Numbers Overview
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