Nonplussed!

Mathematical Proof of Implausible Ideas
Erscheinungsjahr 2010
ISBN: 978-0-691-14822-9
Verlag: Princeton University Press

Buch, Englisch, 216 Seiten, Format (B × H): 153 mm x 232 mm, Gewicht: 318 g

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.

Autoren/Hrsg.

Havil, Julian

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Populäre Darstellungen der Mathematik

Inhaltsverzeichnis

Preface xi

Acknowledgements xiii

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: Conway's Chequerboard Army 62

Chapter 7: The Toss of a Needle 68

Chapter 8: Torricelli's Trumpet 82

Chapter 9: Nontransitive Effects 92

Chapter 10: A Pursuit Problem 105

Chapter 11: Parrondo's Games 115

Chapter 12: Hyperdimensions 127

Chapter 13: Friday the 13th 151

Chapter 14: Fractran 162

The Motifs 180

Appendix A: The Inclusion-Exclusion Principle 187

Appendix B: The Binomial Inversion Formula 189

Appendix C: Surface Area and Arc Length 193

Index 195

Über Autor(innen)

Havil, Julian
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).