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Chases and Escapes: The Mathematics of Pursuit and Evasion (Princeton Puzzlers) [Paperback]

Paul J. Nahin

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Book Description

22 July 2012 Princeton Puzzlers

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.


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Chases and Escapes: The Mathematics of Pursuit and Evasion (Princeton Puzzlers) + Duelling Idiots and Other Probability Puzzlers (Princeton Puzzlers) + Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills
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Review

"In the 18th century, mathematicians began to tease apart how best to track down and intercept prey, inspired by pirate ships bearing down on merchant vessels. The mathematics is by no means trivial, and quickly becomes fiendish if the merchant ship takes evasive action. This is just one of the colorful problems in Paul Nahin's fascinating history of the mathematics of pursuit, in which he guides us masterfully through the maths itself--think lions and Christians, submarines and torpedoes, and the curvaceous flight of fighter aircraft."--New Scientist

"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

From the Inside Flap

"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 book is a treasure trove of puzzles and an enjoyable read. Nahin's aim is to assemble a varied collection of pursuit-and-evasion problems. Fully worked solutions, from first principles, are presented for each problem. Problems are carefully set in their historical context. I am not aware of another book that covers pursuit-and-evasion problems in anywhere near as much detail as is presented here."--Nick Hobson, creator of the award-winning Web site Nick's Mathematical Puzzles

"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

--This text refers to the Hardcover edition.

Inside This Book (Learn More)
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Front Cover | Copyright | Table of Contents | Excerpt | Index
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Customer Reviews

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Amazon.com: 4.5 out of 5 stars  6 reviews
16 of 16 people found the following review helpful
4.0 out of 5 stars Pursuit Problems 25 Nov 2008
By Y. He - Published on Amazon.com
Format:Hardcover|Verified Purchase
Suppose 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.
8 of 11 people found the following review helpful
4.0 out of 5 stars Excellent book, but lacking some intuitive interpretation. 11 May 2009
By Giovanni M. Ciriani - Published on Amazon.com
Format:Hardcover
This 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.
1 of 1 people found the following review helpful
5.0 out of 5 stars A Fascinating Application of Mathematics 1 April 2014
By Marks - Published on Amazon.com
Format:Hardcover
Pursuit 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.
1 of 1 people found the following review helpful
5.0 out of 5 stars Great! 15 Dec 2013
By Paul Alan Safier - Published on Amazon.com
Format:Hardcover|Verified Purchase
Awesome little book on a very interesting subject!! The author does an excellent job with this easy to read gem.
5.0 out of 5 stars More Paul Nahin: it’s good maths! 21 Jun 2014
By Amazon Customer - Published on Amazon.com
Format:Paperback|Verified Purchase
Whenever 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!
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