Mathematical Proof of Implausible Ideas
Buch, Englisch, 216 Seiten, Format (B × H): 153 mm x 232 mm, Gewicht: 318 g
ISBN: 978-0-691-14822-9
Verlag: Princeton University Press
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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Weitere Infos & Material
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
