The Penguin Book of Curious and Interesting Numbers: Revised Edition (英語) ペーパーバック – 1998/5/1
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This dictionary of numbers, arranged in order of magnitude, exposes the fascinating facts about certain numbers and number sequences. The aim of the book is to entertain and enthral the reader, which it certainly does.
DAVID WELLS has written extensively on problems and popular mathematics, and many of his titles are available in Penguin. He is involved in education through writing and research, and lives in this country.
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Usually it takes a great deal of insight as well as considerable mathematical training to discover a yet unknown properties of some number. Only recognizing the beauty of a number pattern is much easier, though, especially with a friendly book like this one on hand. Wells, a long-time mathematics popularizer, has collected over 1000 numbers he considers interesting. Each of them is given a short explanation, often accompanied with a bibliographic reference. Celebrities among the numbers, like i, e or Pi, are given a more comprehensive treatment. Included are also several sequences, like Fibonacci's, Mersenne's, Fermat's, Carmichael's or Kaprekar's, each accompanied with its explanation. So are cyclic, amicable, untouchable or lucky numbers, and many more sequences you probably didn't know about.
While Wells' dictionary certainly gives the impression of a well-researched work, the list of numbers is by no means exhaustive. Anyone familiar with chaos theory will notice the absence of Feigenbaum constant; prime hunters would probably be interested in discussion on Woodall primes, Sophie-Germain primes, or Proth primes. But they are better off with Paulo Ribenboim's book on primes, anyway, while Wells' book, with its easily understandable explanations and accessible price is probably more suited for the "recreational mathematics" audience.
I wanted to dock this half a star. I also wanted to seek out David Wells and shake him down, because ... a number of entries mention a function, phi(n) (this is not "the golden ratio," by the way, although that phi is also discussed in this book). I had no idea what this function was or entailed, so checked in the index, according to which the function is defined under the entry for the number 30. I repaired to the entry for the number 30 and found ... no such definition. Aiee! I looked again. And again. Could not find it. There _is_ an anomalous blank line in the paragraph under the heading '30' ... perhaps it was there and somehow got dropped (and never re-inserted) in a reprinting? I don't know.
I eventually looked the function up in other books, and it IS interesting ... but what happened to Well's entry?
Eventually I will have read through the entire book and, if it is in there somewhere, I will find it -- and come back here to update this review (either that or someone will point out to me where it is).
UPDATE 11.2.12: Of course I found it -- it is defined, along with a number of other functions / things, in the Glossary at the front of the book.
I should also add that the Kindle edition should be avoided. My experience with Kindle + mathematical content has been woeful.