Chases and escapes : the mathematics of pursuit and evasion / Paul J. Nahin, with a new preface by the author.

"Third printing, and first paperback printing, with a new preface, for the Princeton Puzzlers series, 2012."

Includes bibliographical references and index.

Cover; Introduction; Title Page; Copyright Page; Dedication Page; Table of Contents; Preface to the Paperback Edition; What You Need to Know to Read This Book (and How I Learned What I Needed to Know to Write It); Chapter 1. The Classic Pursuit Problem; 1.1 Pierre Bouguer's Pirate Ship Analysis; 1.2 A Modern Twist on Bouguer; 1.3 Before Bouguer: The Tractrix; 1.4 The Myth of Leonardo da Vinci; 1.5 Apollonius Pursuit and Ramchundra's Intercept Problem; Chapter 2. Pursuit of (Mostly) Maneuvering Targets; 2.1 Hathaway's Dog-and-Duck Circular Pursuit Problem.

2.2 Computer Solution of Hathaway's Pursuit Problem2.3 Velocity and Acceleration Calculations for a Moving Body; 2.4 Houghton's Problem: A Circular Pursuit That Is Solvable in Closed Form; 2.5 Pursuit of Invisible Targets; 2.6 Proportional Navigation; Chapter 3. Cyclic Pursuit; 3.1 A Brief History of the n-Bug Problem, and Why It Is of Practical Interest; 3.2 The Symmetrical n-Bug Problem; 3.3 Morley's Nonsymmetrical 3-Bug Problem; Chapter 4. Seven Classic Evasion Problems; 4.1 The Lady-in-the-Lake Problem; 4.2 Isaacs's Guarding-the-Target Problem; 4.3 The Hiding Path Problem.

4.4 The Hidden Object Problem: Pursuit and Evasion as a Simple Two-Person, Zero-Sum Game of Attack-and-Defend4.5 The Discrete Search Game for a Stationary Evader -- Hunting for Hiding Submarines; 4.6 A Discrete Search Game with a Mobile Evader -- Isaacs's Princess-and-Monster Problem; 4.7 Rado's Lion-and-Man Problem and Besicovitch's Astonishing Solution; Appendix A: Solution to the Challenge Problems of Section 1.1; Appendix B: Solutions to the Challenge Problems of Section 1.2; Appendix C: Solution to the Challenge Problem of Section 1.5.

Appendix D: Solution to the Challenge Problem of Section 2.2Appendix E: Solution to the Challenge Problem of Section 2.3; Appendix F: Solution to the Challenge Problem of Section 2.5; Appendix G: Solution to the Challenge Problem of Section 3.2; Appendix H: Solution to the Challenge Problem of Section 4.3; Appendix I: Solution to the Challenge Problem of Section 4.4; Appendix J: Solution to the Challenge Problem of Section 4.7; Appendix K: Guelman's Proof; Notes; Bibliography; Acknowledgments; Index.

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 a.

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