Chases and Escapes

by Nahin, Paul J.

• ISBN13: 9780691125145
• ISBN10: 0691125147
• Format: Hardcover
• Copyright: 2007-07-02
• Publisher: Princeton Univ Pr

Summary

We all played tag when we were kids. The rules couldn't be easier--one player is designated "it" and must try to tag out one of the others. 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 at play in military strategy, high-seas chases by the Coast Guard, even romantic pursuits. InChases and Escapes, Paul Nahin gives us the first complete history of this fascinating area of mathematics. Writing in an accessible style that has been enjoyed by popular-math enthusiasts everywhere, Nahin traces the development of modern pursuit theory from its classical analytical beginnings to the present day. Along the way, he informs his mathematical discussions with fun facts and captivating stories. Nahin invites readers to explore the different approaches to solving various chase-and-escape problems. He draws upon game theory, geometry, linear algebra, target-tracking algorithms--and much more. Nahin offers an array of challenging puzzles for beginners on up, providing historical background for each problem and explaining how each one can be applied more broadly.Chases and Escapesincludes solutions to all problems and provides computer programs that readers can use for their own cutting-edge analysis. This informative and entertaining book is the first comprehensive treatment of the subject, one that is sure to appeal to anyone interested in the mathematics that underlie the all-too-human endeavor of pursuit and evasion.

Table of Contents

What You Need to Know to Read This Book (and How I Learned What I Needed to Know to Write It)	p. xiii
Introduction	p. 1
The Classic Pursuit Problem	p. 7
Pierre Bouguer's Pirate Ship Analysis	p. 7
A Modern Twist on Bouguer	p. 17
Before Bouguer: The Tractrix	p. 23
The Myth of Leonardo da Vinci	p. 27
Apollonius Pursuit and Ramchundra's Intercept Problem	p. 29
Pursuit of (Mostly) Maneuvering Targets	p. 41
Hathaway's Dog-and-Duck Circular Pursuit Problem	p. 41
Computer Solution of Hathaway's Pursuit Problem	p. 52
Velocity and Acceleration Calculations for a Moving Body	p. 64
Houghton's Problem: A Circular Pursuit That Is Solvable in Closed Form	p. 78
Pursuit of Invisible Targets	p. 85
Proportional Navigation	p. 93
Cyclic Pursuit	p. 106
A Brief History of the n-Bug Problem, and Why It Is of Practical Interest	p. 106
The Symmetrical n-Bug Problem	p. 110
Morley's Nonsymmetrical 3-Bug Problem	p. 116
Seven Classic Evasion Problems	p. 128
The Lady-in-the-Lake Problem	p. 128
Isaacs's Guarding-the-Target Problem	p. 138
The Hiding Path Problem	p. 143
The Hidden Object Problem: Pursuit and Evasion as a Simple Two-Person, Zero-Sum Game of Attack-and-Defend	p. 156
The Discrete Search Game for a Stationary Evader - Hunting for Hiding Submarines	p. 168
A Discrete Search Game with a Mobile Evader - Isaacs's Princess-and-Monster Problem	p. 174
Rado's Lion-and-Man Problem and Besicovitch's Astonishing Solution	p. 181
Solution to the Challenge Problems of Section 1.1	p. 187
Solutions to the Challenge Problems of Section 1.2	p. 190
Solution to the Challenge Problem of Section 1.5	p. 198
Solution to the Challenge Problem of Section 2.2	p. 202
Solution to the Challenge Problem of Section 2.3	p. 209
Solution to the Challenge Problem of Section 2.5	p. 214
Solution to the Challenge Problem of Section 3.2	p. 217
Solution to the Challenge Problem of Section 4.3	p. 219
Solution to the Challenge Problem of Section 4.4	p. 222
Solution to the Challenge Problem of Section 4.7	p. 224
Guelman's Proof	p. 229
Notes	p. 235
Bibliography	p. 245
Acknowledgments	p. 249
Index	p. 251
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