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Nonplussed! Mathematical Proof of Implausible Ideas

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Nonplussed! Mathematical Proof of Implausible Ideas Cover

 

Synopses & Reviews

Publisher Comments:

"Nonplussed!, as the title suggests, is a marvelous study of some two dozen choice mathematical problems that boggle the mind. Unlike so many books on recreational math, Havil doesn't hesitate to give crystal-clear proofs and their necessary equations. John Conway's great checker-jumping puzzle is here, along with amazing nontransitive betting paradoxes and other confounding results almost impossible to believe. No one interested in recreational mathematics on an intermediate advanced level should pass up this stimulating, delightful volume."--Martin Gardner

"In Nonplussed!, his new book of fascinating discussions of mathematical questions, Julian Havil's literary signature is evident even without seeing his name on the cover. The presentation always displays his strong ability to weave together the historical with what is often a surprising mathematical twist, even for those problems that have been around long enough to be called classic. Nonplussed! will be a classic, too."--Paul J. Nahin, author of Dr. Euler's Fabulous Formula

"Nonplussed!! is a very interesting and eclectic mix of paradoxes that has the potential to be a very useful and lasting contribution to popular mathematics."--Christopher J. Sangwin, author of Mathematics Galore

"I greatly enjoyed this book and I imagine that anyone who liked high school math will too. Nonplussed! certainly succeeds in surprising-and in giving insightful proofs of the mathematical results discussed. It is a magnificent demonstration of how far even rather straightforward mathematics can take you. And by describing many of the historical characters involved and the problems that motivated them, it makes mathematics seem like an adventure."--Nick Huggett, author of Space from Zeno to Einstein

Synopsis:

"Nonplussed!, as the title suggests, is a marvelous study of some two dozen choice mathematical problems that boggle the mind. Unlike so many books on recreational math, Havil doesn't hesitate to give crystal-clear proofs and their necessary equations. John Conway's great checker-jumping puzzle is here, along with amazing nontransitive betting paradoxes and other confounding results almost impossible to believe. No one interested in recreational mathematics on an intermediate advanced level should pass up this stimulating, delightful volume."--Martin Gardner

"In Nonplussed!, his new book of fascinating discussions of mathematical questions, Julian Havil's literary signature is evident even without seeing his name on the cover. The presentation always displays his strong ability to weave together the historical with what is often a surprising mathematical twist, even for those problems that have been around long enough to be called classic. Nonplussed! will be a classic, too."--Paul J. Nahin, author of Dr. Euler's Fabulous Formula

"Nonplussed!! is a very interesting and eclectic mix of paradoxes that has the potential to be a very useful and lasting contribution to popular mathematics."--Christopher J. Sangwin, author of Mathematics Galore

"I greatly enjoyed this book and I imagine that anyone who liked high school math will too. Nonplussed! certainly succeeds in surprising-and in giving insightful proofs of the mathematical results discussed. It is a magnificent demonstration of how far even rather straightforward mathematics can take you. And by describing many of the historical characters involved and the problems that motivated them, it makes mathematics seem like an adventure."--Nick Huggett, author of Space from Zeno to Einstein

Synopsis:

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.

About the Author

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).

Table of 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

Product Details

ISBN:
9780691148229
Author:
Havil, Julian
Publisher:
Princeton University Press
Subject:
Applied
Subject:
Applied Sciences
Subject:
Mathematics
Subject:
Physics
Subject:
Mathematics-Games and Puzzles
Subject:
Popular science
Copyright:
Edition Description:
Trade paper
Publication Date:
20100831
Binding:
TRADE PAPER
Language:
English
Illustrations:
18 halftones. 143 line illus.
Pages:
216
Dimensions:
9 x 6 in 11 oz

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Related Subjects

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Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Popular Surveys and Recreational

Nonplussed! Mathematical Proof of Implausible Ideas Used Trade Paper
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Product details 216 pages Princeton University Press - English 9780691148229 Reviews:
"Synopsis" by , "Nonplussed!, as the title suggests, is a marvelous study of some two dozen choice mathematical problems that boggle the mind. Unlike so many books on recreational math, Havil doesn't hesitate to give crystal-clear proofs and their necessary equations. John Conway's great checker-jumping puzzle is here, along with amazing nontransitive betting paradoxes and other confounding results almost impossible to believe. No one interested in recreational mathematics on an intermediate advanced level should pass up this stimulating, delightful volume."--Martin Gardner

"In Nonplussed!, his new book of fascinating discussions of mathematical questions, Julian Havil's literary signature is evident even without seeing his name on the cover. The presentation always displays his strong ability to weave together the historical with what is often a surprising mathematical twist, even for those problems that have been around long enough to be called classic. Nonplussed! will be a classic, too."--Paul J. Nahin, author of Dr. Euler's Fabulous Formula

"Nonplussed!! is a very interesting and eclectic mix of paradoxes that has the potential to be a very useful and lasting contribution to popular mathematics."--Christopher J. Sangwin, author of Mathematics Galore

"I greatly enjoyed this book and I imagine that anyone who liked high school math will too. Nonplussed! certainly succeeds in surprising-and in giving insightful proofs of the mathematical results discussed. It is a magnificent demonstration of how far even rather straightforward mathematics can take you. And by describing many of the historical characters involved and the problems that motivated them, it makes mathematics seem like an adventure."--Nick Huggett, author of Space from Zeno to Einstein

"Synopsis" by , 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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