Nonplussed!: Mathematical Proof of Implausible IdeasPrinceton 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. |
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 |