Nonplussed!: Mathematical Proof of Implausible Ideas

Első borító
Princeton University Press, 2010. aug. 2. - 216 oldal

Math—the application of reasonable logic to reasonable assumptions—usually produces reasonable results. But sometimes math generates astonishing paradoxes—conclusions that seem completely unreasonable or just plain impossible but that are nevertheless demonstrably true. Did you know that a losing sports team can become a winning one by adding worse players than its opponents? Or that the thirteenth of the month is more likely to be a Friday than any other day? Or that cones can roll unaided uphill? In Nonplussed!—a delightfully eclectic collection of paradoxes from many different areas of math—popular-math writer Julian Havil reveals the math that shows the truth of these and many other unbelievable ideas.

Nonplussed! pays special attention to problems from probability and statistics, areas where intuition can easily be wrong. These problems include the vagaries of tennis scoring, what can be deduced from tossing a needle, and disadvantageous games that form winning combinations. Other chapters address everything from the historically important Torricelli's Trumpet to the mind-warping implications of objects that live on high dimensions. Readers learn about the colorful history and people associated with many of these problems in addition to their mathematical proofs.

Nonplussed! will appeal to anyone with a calculus background who enjoys popular math books or puzzles.

 

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Real proofs of a selection of nonintuitive, college-level, recreational math results, half of them involving probability. Not a fat book, but digesting every equation would make for a long reading time. Teljes értékelés elolvasása

Kiválasztott oldalak

Tartalomjegyzék

Introduction
1
CHAPTER 1 Three Tennis Paradoxes
4
CHAPTER 2 The Uphill Roller
16
CHAPTER 3 The Birthday Paradox
25
CHAPTER 4 The spin of a Table
37
CHAPTER 5 Derangements
46
CHAPTER 6 Conways Chequerboard Army
62
CHAPTER 7 The Toss of a Needle
68
CHAPTER 11 Parrondos Games
115
CHAPTER 12 Hyperdimensions
127
CHAPTER 13 Friday the 13th
151
CHAPTER 14 Fractran
162
THE MOTIFS
180
APPENDIX A The InclusionExclusion Principle
187
APPENDIX B The Binomial Inversion Formula
189
APPENDIX C Surface Area and Arc Length
193

CHAPTER 8 Torricells Trumpet
82
CHAPTER 9 Nontransitive Effects
92
CHAPTER 10 A Pursuit Problem
105

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A szerzőről (2010)

Julian Havil is a former Master at Winchester College, England, where he taught mathematics for more than thirty years. He is the author of Gamma: Exploring Euler's Constant and Impossible?: Surprising Solutions to Counterintuitive Conundrums (both Princeton).

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