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Professor Stewart's Cabinet of Mathematical Curiosities Paperback – Illustrated, January 6, 2009
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"Stewart has a genius for explanation that allows details of the Poincaré conjecture and Riemann hypothesis to sit happily alongside a quip about a chicken crossing a Möbius strip.... Mathematics doesn't come more entertaining than this."―New Scientist
"The exciting side of math--puzzles, games and thrilling oddities."―
"What positive integer is equal to its own Scrabble score when spelled out in full? Stewart...offers this and a hodgepodge of other puzzles, paradoxes, brainteasers, tricks, facts and jokes, which he accurately calls 'curiosities.'."―Science News
"Open one of the 179 'drawers' in Professor Stewart's cabinet, and you might find just a one-liner...or a seven-page essay on Fermat's last theorem.... The book can be devoured in one giant gulp or savored, one curiosity at a time."―IEEE Spectrum
- Item Weight : 11.2 ounces
- Paperback : 320 pages
- ISBN-10 : 0465013023
- ISBN-13 : 978-0465013029
- Product Dimensions : 5.5 x 0.75 x 8.25 inches
- Publisher : Basic Books (January 6, 2009)
- Language: : English
- Best Sellers Rank: #773,740 in Books (See Top 100 in Books)
- Customer Reviews:
Top reviews from the United States
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The approach it takes is to tackle any subject at all in a series of short essays or even paragraphs. These subjects can be anything from the typical logic puzzles (the first one is that you meet three people on an alien planet. There are two types: those who only tell the truth, and those who only lie. How do you tell who is who after asking them one question each?) all the way to the uses of fractal geometry and advanced mathematical concepts like the P=NP? problem which has a $1 million dollar prize of you can prove, or disprove it. Along the way are strewn things like brief histories of famout mathematicians and all kinds of additional trivia that can be shoved into a 250 page paperback.
To those who insist on findind the answers to the various puzzles throughout the book, the author includes a 50 page appendix which contains all the answers and more explanations on how to reach them.
This book is suitable for anyone who has gone beyond basic algebra in school and is not so esoteric as to be chock full of too much difficult notations. On the other hand, there are many segments that are thrown in that are either old chestnuts or so advanced as to be incomprehensible to most people. While I understood 98% of the book, the additional 2% made my eyes glaze over which is why I did not give this book all five stars. What was missing for me, to make it into a five star book, was some sort of spark and connectivity around all these different topics that would tie them all together. The only tie in to be found is that it's all related to mathematics, and that was just not sufficient.
Overall, I would give this book to someone with a passing interest in math as a book that can be read in sections and segments when the mood strikes, but not one that you either need to read in one session, nor one that should immediately go on top of your personal reading pile.
There are rings on the coat of arms of the Borromeo family, three rings that you cannot pull apart but none of which is linked to another. There is a section on famous mathematicians who aren't famous for being mathematicians. Sure, you knew Lewis Carroll, famous for the _Alice_ books, was a mathematician / logician, but did you know Art Garfunkel got his master's in math, and only stopped work on his PhD so he could pursue his singing career? Bram Stoker, author of _Dracula_, had a mathematics degree. Leon Trotsky had his mathematical career ended by exile to Siberia. There is a section on Fermat's famous Last Theorem and how it was proved fifteen years ago by complicated modern methods. Fermat himself could not have used such methods in the proof he said he had, but he did not write it down because he didn't have enough space in the margin in which he was writing notes. Stewart says that there might be a simpler proof, and while he repeatedly encourages readers to branch out on their own from these problems, he warns them about coming up with proofs for this one, and he also hints at the frustrations of being a public mathematician: "If you think you've found it, _please don't send it to me_. I get too many attempted proofs as it is, and so far - well, just don't get me started, OK?" There is a section on dividing a cake fairly. It's easy with two people - one cuts the cake and the other gets to decide which piece to take. How do you extend this to three people? If you have a block of cheese in cube form, how can you cut it so that the cut face is hexagonal? Why in lists of numerical data, like the areas of each of the fifty states, are the numbers far more likely to start with 1 or 2 rather than 8 or 9? And how can this be true whether the numbers represent square miles, square kilometers, acres, or any other measurement? What shape of road would give a smooth ride to a bicycle with square wheels? A person born in 35 BC died after his birthday in 35 AD; how old was he? (Hint: those ancients could do math, but they didn't have the concept of 0.) What number, spelled out in Scrabble tiles, equals its Scrabble score? This delightful book is a real miscellany.
It also has one characteristic those older recreational math books didn't have: internet references. When discussing, for instance, John Horton Conway's fascinating complexity-from-simplicity game Life, Stewart can send the reader to an internet version "which is easy to use and will give hours of pleasure." Some of the references are merely to Wikipedia, but others are to specialty sites, including the extensive Wolfram Mathworld. This would be a wonderful book to give to any young person, especially one who claims not to like math. Stewart may not have a cure for such a condition, but his fine collection of amusements could demonstrate that such abhorrence is at least sometimes misdirected.
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So my initial advice for any readers of this would be get a notepad and some pens and keep them nearby. Fans of recreational mathematics will find much that is familiar here, as some problems recur in just about every such 'popular' level book on maths, such as the problem of the bridges of Konigsberg or lots of factoids about pi.
That may sound like damning with faint praise, but there is a depth of mathematics on display here that is rather splendid. Many of the ideas are really quite profound, yet the way they are presented makes them quite accessible. A non mathematician might disagree with me, but it may be interesting to find out from others if there are areas where they get stuck.
There is a general trend for the puzzles to get a little bit more difficult later on in the book. So we are given some treats that will be unfamiliar even to those who did maths at A-level. We deal with topics ranging from geometry, number theory, topology and even some complexity is thrown in at the end.
I probably ought to add that for any sections that ask questions there are answers provided at the back of the book. Most are pretty good, though if the book does have any weaknesses, it is here, where some of the answers are given with not enough explanation. Though for recreational mathematics, one of the litmus tests has to be how well the solution to the Monty Hall problem is described and this one is very fair.
There is a follow-up book that Ian Stewart wrote, in the same vein but with a different set of problems. Given the quality of this work, I will be reading that as well, so you can look forward to seeing another review like this when I get around to it.
I think overall I enjoyed it though.