Chases and Escapes: The Mathematics of Pursuit and Evasion

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Princeton University Press, 2007 - Mathematics - 253 pages
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"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

 

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Contents

Introduction
1
The Classic Pursuit Problem
7
12 A Modern Twist on Bouguer
17
The Tractrix
23
14 The Myth of Leonardo da Vinci
27
15 Apollonius Pursuit and Ramchundras Intercept Problem
29
Pursuit of Mostly Maneuvering Targets
41
22 Computer Solution of Hathaways Pursuit Problem
52
45 The Discrete Search Game for a Stationary Evader Hunting for Hiding Submarines
168
46 A Discrete Search Game with a Mobile Evader Isaacss PrincessandMonster Problem
174
47 Rados LionandMan Problem and Besicovitchs Astonishing Solution
181
Solution to the Challenge Problems of Section 11
187
Solutions to the Challenge Problems of Section 12
190
Solution to the Challenge Problem of Section 15
198
Solution to the Challenge Problem of Section 22
202
Solution to the Challenge Problem of Section 23
209

23 Velocity and Acceleration Calculations for a Moving Body
64
A Circular Pursuit That Is Solvable in Closed Form
78
25 Pursuit of Invisible Targets
85
26 Proportional Navigation
93
Cyclic Pursuit
106
32 The Symmetrical nBug Problem
110
33 Morleys Nonsymmetrical 3Bug Problem
116
Seven Classic Evasian Problems
128
42 Isaacss GuardingtheTarget Problem
138
43 The Hiding Path Problem
143
Pursuit and Evasion as a Simple TwoPerson ZeroSum Game of AttackandDefend
156
Solution to the Challenge Problem of Section 25
214
Solution to the Challenge Problem of Section 32
217
Solution to the Challenge Problem of Section 43
219
Solution to the Challenge Problem of Section 44
222
Solution to the Challenge Problem of Section 47
224
Guelmans Proof
229
Notes
235
Bibliography
245
Acknowledgments
249
Index
251
Copyright

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About the author (2007)

Paul J. Nahin is professor emeritus of electrical engineering at the University of New Hampshire. He is the best-selling author of many popular-math books, including "Duelling Idiots and Other Probability Puzzlers", "The Logician and the Engineer", "Number-Crunching", "Mrs. Perkins s Electric Quilt", and "An Imaginary Tale" (all Princeton).

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