Impossible?

Surprising Solutions to Counterintuitive Conundrums

Julian Havil

• Publisher: Princeton University Press
• Year: 2011
• Print ISBN: 9780691150024, 9780691131313
• eBook ISBN: 9781400829675
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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.

Table of contents

• Cover
• Half title
• Title
• Copyright
• Dedication
• Contents
• Acknowledgments
• Introduction
• Chapter 1. It’s Common Knowledge
• Chapter 2. Simpson’s Paradox
• Chapter 3. The Impossible Problem
• Chapter 4. Braess’s Paradox
• Chapter 5. The Power of Complex Numbers
• Chapter 6. Bucking the Odds
• Chapter 7. Cantor’s Paradise
• Chapter 8. Gamow–Stern Elevators
• Chapter 9. The Toss of a Coin
• Chapter 10. Wild-Card Poker
• Chapter 11. Two Series
• Chapter 12. Two Card Tricks
• Chapter 13. The Spin of a Needle
• Chapter 14. The Best Choice
• Chapter 15. The Power of Powers
• Chapter 16. Benford’s Law
• Chapter 17. Goodstein Sequences
• Chapter 18. The Banach–Tarski Paradox
• The Motifs
• Appendix
• Index