Chases and Escapes: The Mathematics of Pursuit and Evasion

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Princeton University Press, 2012 - Mathematics - 253 pages
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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.


 

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Contents

Chapter 1 The Classic Pursuit Problem
7
Chapter 2 Pursuit of Mostly Maneuvering Targets
41
Chapter 3 Cyclic Pursuit
106
Chapter 4 Seven Classic Evasion Problems
128
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 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

Solution to the Challenge Problem of Section 23
209
Solution to the Challenge Problem of Section 25
214

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About the author (2012)

Paul J. Nahin is the author of many best-selling popular-math books, including "Chases and Escapes," "Dr. Euler's Fabulous Formula," "When Least is Best," "Duelling Idiots and Other Probability Puzzlers," and "An Imaginary Tale" (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.

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