Nonplussed! Mathematical Proof of Implaussible Ideas

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: Conclusions that, for example, tell us 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.
Contents: 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