Impossible? (ebook)

Argumento de Impossible? (ebook)

"This sequel to the author's book Nonplussed! supplies another set of brain-stretching problems and ideas. Its subtitle is 'Surprising Solutions to Counterintuitive Conundrums'; the surprise often consisting of the fact that it is possible to obtain a solution at all! . . . This is another excellent book by Havil, following in the Martin Gardner tradition."--Alan Stevens, Mathematics Today

"I would highly recommend this book as a reference for the mathematician who likes recreational mathematics, or as a good read for the recreational enthusiast with a penchant for more rigor."--Blair Madore, MAA Reviews

"Julian Havil has quietly joined the ranks of the very best writers of popular mathematics. His two volume set Impossible? and Nonplussed! Mathematical Proof of Implausible Ideas not only belong in every library, but in the hands of every young person interested in mathematics and especially in the hands of their teachers."--John J. Watkins, Mathematical Intelligencer

"Julian Havil's Impossible? is a superb discussion of problems easily understood by a high schooler, yet with solutions so counterintuitive as to seem impossible. Topics include the notorious Monty Hall three-door problem, the Gamow-Stern elevator paradoxes, the Kruskal count card trick, Cantor's 'paradise' of alephs, and the mind-blowing Banach-Tarski paradox, all analyzed in depth by a master who does not hold back equations that provide elegant proofs. There are surprises on almost every page."--Martin Gardner

"This book is a fascinating and thoroughly enjoyable read. Havil offers an engaging collection of counterintuitive results and seemingly impossible problems. Some of the material is truly astonishing, and the author conveys his sense of surprise very effectively. Each problem ultimately yields to careful and well-presented analysis. The history of many of the results is discussed, and further references are provided."--Nick Hobson, creator of the award-winning Web site Nick's Mathematical Puzzles

"I thought it impossible for Julian Havil to exceed Nonplussed!, his previous collection of perplexing math puzzlers. And yet he has done just that with the sequel Impossible?, an accomplishment that has left me nonplussed."--Paul J. Nahin, author of An Imaginary Tale

"Havil once again explores a variety of mathematical results and problems that at first appear to be self-contradictory, or stated in such a way that no solution could exist. In each case, he then either sketches a proof of why the result is not contradictory, or explains the solution to the seemingly unsolvable problem . . . . Like a magician revealing secrets, Havil maintains this sense through most chapters, dropping the punch line at just the right moment."--J.T. Noonan, Choice

"Impossible? is an immensely thought-provoking book. Even if you skim or skip the more complex abstract math, you may have a hard time letting these puzzles go, so strongly do they flout common sense. You'll just have to do your best to put them our of your mind when you need to get some sleep, but if the situation ever arises, be sure to take Monty up on his offer."--Ray Bert, Civil Engineering0Acknowledgments xi
Introduction 1
Chapter 1: It's Common Knowledge 3
Chapter 2: Simpson's Paradox 11
Chapter 3: The Impossible Problem 21
Chapter 4: Braess's Paradox 31
Chapter 5: The Power of Complex Numbers 39
Chapter 6: Bucking the Odds 50
Chapter 7: Cantor's Paradise 68
Chapter 8: Gamow-Stern Elevators 82
Chapter 9: The Toss of a Coin 88
Chapter 10: Wild-Card Poker 103
Chapter 11: Two Series 113
Chapter 12: Two Card Tricks 131
Chapter 13: The Spin of a Needle 146
Chapter 14: The Best Choice 165
Chapter 15: The Power of Powers 176
Chapter 16: Benford's Law 190
Chapter 17: Goodstein Sequences 201
Chapter 18: The Banach-Tarski Paradox 210
The Motifs 217
Appendix 221
Index 233