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Chases and Escapes: The Mathematics of Pursuit and Evasion (Princeton Puzzlers) Paperback – July 22, 2012
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We all played tag when we were kids. What most of us don't realize is that this simple chase game is in fact an application of pursuit theory, and that the same principles of games like tag, dodgeball, and hide-and-seek are also at play in military strategy, high-seas chases by the Coast Guard, and even romantic pursuits. In Chases and Escapes, Paul Nahin gives us the first complete history of this fascinating area of mathematics, from its classical analytical beginnings to the present day.
Drawing on game theory, geometry, linear algebra, target-tracking algorithms, and much more, Nahin also offers an array of challenging puzzles with their historical background and broader applications. Chases and Escapes includes solutions to all problems and provides computer programs that readers can use for their own cutting-edge analysis.
Now with a gripping new preface on how the Enola Gay escaped the shock wave from the atomic bomb dropped on Hiroshima, this book will appeal to anyone interested in the mathematics that underlie pursuit and evasion.
- Print length272 pages
- LanguageEnglish
- Publication dateJuly 22, 2012
- Dimensions5.51 x 0.65 x 8.35 inches
- ISBN-100691155011
- ISBN-13978-0691155012
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Editorial Reviews
Review
"This is a highly readable book that offers several colorful applications of differential equations and good examples of non-trivial integrals for calculus students. It would be a good source of examples for the classroom and or a starting point for an independent project."---Bill Satzer, MAA Review
"This book contains a well-written, well-organized collection of solutions to twenty-one challenging calculus and differential equation problems that concern pursuit and evasion as well as the historical background of each problem type." ― Mathematics Teacher
"I am sure that this book will appeal to everyone who is interested in mathematics and game theory. Excellent work."---Prabhat Kumar Mahanti, Zentralblatt Math
"Chases and Escapes is a wonderful collection of interesting and classic pursuit and evasion problems. . . . If you are interested in in dogs chasing ducks, pirates chasing merchants, and submarines hiding, then this book is for you." ― Mathematics Teacher
Review
"I know of no better way to grasp the basic concepts of calculus than to study pursuit-and-escape problems. Paul Nahin has made a superb survey of the vast field of such problems, from Zeno's paradox of Achilles and the tortoise through the famous four bugs that once made the cover of Scientific American. Not only does he make clear the required differential equations, but he traces each problem's colorful history. No book on the topic could be more definitive or a greater pleasure to read."―Martin Gardner
"Chases and Escapes is a superb treatment of the solutions to a variety of pursuit-evasion problems, some classic and others more contemporary. The content is accessible to undergraduates in mathematics or the physical sciences, with lots of supporting detail included. The author's lively writing style makes for enjoyable reading."―David M. Burton, University of New Hampshire
"This is a well-written and novel book that is comprehensively researched and enthusiastically presented. Nahin offers a very good mixture of elegant math and lively historical interludes. I wasn't aware the topic had such a rich history and wide scope."―Desmond Higham, University of Strathclyde
From the Back Cover
"Nahin provides beautiful applications of calculus, differential equations, and game theory. If you are pursuing an enjoyable collection of mathematical problems and the stories behind them, then your search ends here."--Arthur Benjamin, Harvey Mudd College
"I know of no better way to grasp the basic concepts of calculus than to study pursuit-and-escape problems. Paul Nahin has made a superb survey of the vast field of such problems, from Zeno's paradox of Achilles and the tortoise through the famous four bugs that once made the cover of Scientific American. Not only does he make clear the required differential equations, but he traces each problem's colorful history. No book on the topic could be more definitive or a greater pleasure to read."--Martin Gardner
"Chases and Escapes is a superb treatment of the solutions to a variety of pursuit-evasion problems, some classic and others more contemporary. The content is accessible to undergraduates in mathematics or the physical sciences, with lots of supporting detail included. The author's lively writing style makes for enjoyable reading."--David M. Burton, University of New Hampshire
"This is a well-written and novel book that is comprehensively researched and enthusiastically presented. Nahin offers a very good mixture of elegant math and lively historical interludes. I wasn't aware the topic had such a rich history and wide scope."--Desmond Higham, University of Strathclyde
About the Author
Product details
- Publisher : Princeton University Press; Revised edition (July 22, 2012)
- Language : English
- Paperback : 272 pages
- ISBN-10 : 0691155011
- ISBN-13 : 978-0691155012
- Item Weight : 9.9 ounces
- Dimensions : 5.51 x 0.65 x 8.35 inches
- Best Sellers Rank: #2,098,833 in Books (See Top 100 in Books)
- #432 in Game Theory (Books)
- #1,251 in Math Games
- #1,291 in Mathematics History
- Customer Reviews:
About the author
Paul Nahin was born in California, and did all his schooling there (Brea-Olinda High 1958, Stanford BS 1962, Caltech MS 1963, and - as a Howard Hughes Staff Doctoral Fellow - UC/Irvine PhD 1972, with all degrees in electrical engineering). He worked as a digital logic designer and radar systems engineer in the Southern California aerospace industry until 1971, when he started his academic career. He has taught at Harvey Mudd College, the Naval Postgraduate School, and the Universities of New Hampshire (where he is now emeritus professor of electrical engineering) and Virginia. In between and here-and-there he spent a post-doctoral year at the Naval Research Laboratory, and a summer and a year at the Center for Naval Analyses and the Institute for Defense Analyses as a weapon systems analyst, all in Washington, DC. He has published a couple dozen short science fiction stories in ANALOG, OMNI, and TWILIGHT ZONE magazines, and has written 24 books on mathematics and physics, published by IEEE Press, Springer, and the university presses of Johns Hopkins and Princeton. Translations of his books in Chinese, Russian, Arabic, Greek, Korean, Spanish, Romanian, and Japanese have appeared. The book THE MATHEMATICAL RADIO was published by Princeton in January 2024 and the book THE PROBABILITY INTEGRAL was published by Springer in October 2023. He has given invited talks on mathematics at the Anja Greer Math and Technology Conference at Phillips Exeter Academy (twice, in 2008 and 2018), as well as at Bowdoin College, the Claremont Graduate School, the University of Tennessee, and Caltech, has appeared on National Public Radio's "Science Friday" show (discussing time travel) as well as on New Hampshire Public Radio's "The Front Porch" show (discussing imaginary numbers), and advised Boston's WGBH Public Television's "Nova" program on the script for their time travel episode. He gave the invited Sampson Lectures for 2011 in Mathematics at Bates College (Lewiston, Maine). He received the 2017 Chandler Davis Prize for Excellence in Expository Writing in Mathematics.
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- Reviewed in the United States on June 21, 2014Whenever you see a Paul Nahin’s book, you may expect something nice, well-written about a theme in mathematics. With an undeniable ability to transform technical subjects into tasty and readable texts (for the layman), this partucular book is a treat for those interested in graph theory. Can’t miss it!
- Reviewed in the United States on May 19, 2016Make sure you've had at least through Calc II if you want to navigate this book! Awesome to have some practical applications for all of it finally though.
- Reviewed in the United States on December 15, 2013Awesome little book on a very interesting subject!! The author does an excellent job with this easy to read gem.
- Reviewed in the United States on November 25, 2008Suppose you are given a problem which says: "Three dogs are placed at the vertices of an equilateral triangle; they run one after the other. What is the curve described by each of them?" How would you solve the problem? If this makes you scratch your head a little, don't worry. This problem actually appeared on the Cambridge University Mathematical Tripos Examination in 1871 and is one of the so-called "n-bug" problem. Obviously when n goes to infinity, the curve of each bug becomes a circle. On p. 110, Professor Nahin started to analyze this problem by writing down the radial and transverse components of the velocity, and step-by-step, he showed us how to solve this seemingly complicated problem, yet only elementary calculus (and perhaps some college physics) is needed. The approach is elegant. This book, which has a subtitle of The Mathematics of Pursuit and Evasion, obviously has a lot of mathematics and many equations, and it is not for general readers who are afraid of math. However, the book provides many elegant pursuit problems with military applications. For those who enjoy the real applications of calculus and perhaps like do some calculations on the back of an envelope, this is a superb book.
- Reviewed in the United States on January 15, 2016very interesting
- Reviewed in the United States on April 1, 2014Pursuit theory has been a favorite mathematical recreation of mine since the early 1990's. In this book, the author explores many continuous and discrete pursuit/evasion situations with clarity and succinctness. I encourage anyone with a background in differential equations to work through the problems in this book. They are rewarding and may very well inspire new discoveries on the subject.
For the lay person, the problems are intriguing in their own right (e.g., "Pursuit of Invisible Targets") but the solutions are derived and expressed mathematically. At the very least, this book presents a truly fascinating application of mathematics to anyone who picks it up.
- Reviewed in the United States on February 13, 2014I found this book interesting, but difficult to understand at times. I read it to apply the principles to law enforcement such as missing persons.
- Reviewed in the United States on May 11, 2009This is an excellent review of the math of pursuit and escape paths. I have not read the book completely, but I concentrated my reading on a couple of problems I was mostly interested in: The Lady in the Lake problem, and the Lion-and-Man problem. These two problems are strictly connected, and have more immediate geometric explanations than the equations of the problems presented in the book. However, these alternative explanations are missing in the book; too bad because they add a lot to the understanding and intuition of the problems. In one case actually, (Lion-and-Man problem), I believe the outcome of the problem is different from the one provided. This doesn't detract from this enjoyable book, which is well written, with very approachable, step-by-step math passages.
Top reviews from other countries
- Enrico T.Reviewed in Italy on October 8, 2023
5.0 out of 5 stars Intriguing.
A well built text on a specific topic, full of curious example of the real life under a sound mathematical approach
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François PReviewed in France on December 4, 2019
5.0 out of 5 stars Excellent livre
Excellent livre, comme quatre autres du même auteur que j'ai pu lire, notamment "In praise of simple physics".
- Andrew MortonReviewed in the United Kingdom on January 8, 2015
5.0 out of 5 stars Five Stars
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