Most Helpful Customer Reviews
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23 of 23 people found the following review helpful:
No recreational mathematician should be without it, 11 Dec 2000
In the foreword to G.H. Hardy's book A Mathematician's Apology, C.P. Snow tells an anecdote about Hardy and his collaborator Srinavasa Ramanujan. Hardy, perhaps the greatest number theorist of 20th century, took a taxi from London to the hospital at Putney where Ramanujan was dying of tuberculosis, Hardy noticed its number, 1729. Always inept about introducing a conversation, he entered the room where Ramanujan was lying in bed and, with scarcely a hello, blurted out his opinion about the taxi-cab number. It was, he declared, "rather a dull number," adding that he hoped that wasn't a bad omen. "No, Hardy! No, Hardy," said Ramanujan, "it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways."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.
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14 of 16 people found the following review helpful:
Doesn't read like a dictionary, 8 May 2003
David Wells has assembled an unique and readable collection of facts about numbers, arranged in numerical order! Entries are fascinating, for the most part, though they can be frustrating, too. For example, when first encountering the notion of automorphic numbers (numbers whose squares end in the same digits as the original number), it is tempting to discover if there are other related entries -- 'trimorphic numbers', for instance? It is possible to track these down using the small index provided and quite fun to do.
Unlike other dictionaries this is best read from front to back though it can be used as a reference, once one is familiar with it.
Many concepts are briefly explained as they are encountered, and some merely referred to in passing, and the frustration here is that there need not be full information in the text. However, this is most enjoyably resolved by brushing up one's own skills and trying to demonstrate the simpler claims for oneself. There is plenty here for the dabbling amateur to try, though the serious mathematician can also enjoy the book.
I have one qualification: David Wells identifies 51 as the least uninteresting number (no, not a contradiction: it is simultaneously interesting and uninteresting, he claims) -- because he cannot find an interesting fact about it. He fails to notice that it is the fourth trimorphic (and non-automorphic) number: 4, 9, 49, 51 and 75 being the first five cases. This means that it is mildly more interesting than at first supposed.
I look forward to a revised edition -- with readers' contributions and comments.
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