Impossible?: Surprising Solutions to Counterintuitive Conundrums

Impossible?: Surprising Solutions to Counterintuitive Conundrums

by Julian Havil
     
 

ISBN-10: 0691131317

ISBN-13: 9780691131313

Pub. Date: 04/01/2008

Publisher: Princeton University Press

In Nonplussed!, popular-math writer Julian Havil delighted readers with a mind-boggling array of implausible yet true mathematical paradoxes. Now Havil is back with Impossible?, another marvelous medley of the utterly confusing, profound, and unbelievable--and all of it mathematically irrefutable.

Whenever Forty-second Street in New York is

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Overview

In Nonplussed!, popular-math writer Julian Havil delighted readers with a mind-boggling array of implausible yet true mathematical paradoxes. Now Havil is back with Impossible?, another marvelous medley of the utterly confusing, profound, and unbelievable--and all of it mathematically irrefutable.

Whenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly--why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion--how is this possible? What does the game show Let's Make A Deal reveal about the unexpected hazards of decision-making? What can the game of cricket teach us about the surprising behavior of the law of averages? These are some of the counterintuitive mathematical occurrences that readers encounter in Impossible?

Havil ventures further than ever into territory where intuition can lead one astray. He gathers entertaining problems from probability and statistics along with an eclectic variety of conundrums and puzzlers from other areas of mathematics, including classics of abstract math like the Banach-Tarski paradox. These problems range in difficulty from easy to highly challenging, yet they can be tackled by anyone with a background in calculus. And the fascinating history and personalities associated with many of the problems are included with their mathematical proofs. Impossible? will delight anyone who wants to have their reason thoroughly confounded in the most astonishing and unpredictable ways.

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Product Details

ISBN-13:
9780691131313
Publisher:
Princeton University Press
Publication date:
04/01/2008
Pages:
264
Product dimensions:
6.30(w) x 9.30(h) x 1.00(d)

Table of Contents


Acknowledgments 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

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