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.
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).
"Nonplussed! is a collection of lovely paradoxes: facts that are provable logically but are nevertheless seriously counterintuitive...It is an exciting book. It should be in every...college library. It would even be the right gift for mathematicians and anyone who uses mathematics--economists, business analysts and many others--and indeed for anyone who would claim to be educated."--Peter M. Neumann, Times Higher Education Supplement
"This is a splendid collection of articles, inspired by Martin Gardner's writings. Old conundrums are given new twists and applications, newer perplexing ideas are described with panache. The forthcoming companion book has a high standard to maintain."--John Haigh, London Mathematical Society Newsletter
"It is therefore recommended that Julian Havil's headmaster award him further sabbatical leave for the purpose of producing a sequel to this welcome addition to the mathematical literature."--Peter Ruane, MAA Review
"A review of a book as good as this must either repeat the positive adjectives other reviewers have used, or require a very large thesaurus. Since I find myself in complete agreement with all of the following words from other reviews, I will repeat them immediately: marvelous, crystal-clear, great, amazing, stimulating, delightful, fascinating, strong, surprising, classic, interesting, eclectic, insightful, magnificent. That one book could encourage such gushing praise seems as unlikely as one book being able to cram in a great variety and depth of mathematical problems, colourful historical anecdotes, significant nods to ethno-mathematics, difficult but well-explained proofs, clear and engaging prose and beautiful diagrams. Yet Havilšs book succeeds on all accounts...The brilliant writing, the wonderful problems, the weaving together of past and future, games and discovery, and world number cultures will have you returning to this ageless book time and again."--Phil Wilson, Plus Magazine
Table of Contents:
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
This book has been translated into:
Other Princeton books authored or coauthored by Julian Havil: