## Chases and Escapes: |

What You Need to Know to Read This Book (and How I Learned What I Needed to Know to Write It) xiii 1.1 Pierre Bouguer's Pirate Ship Analysis 7 1.2 A Modern Twist on Bouguer 17 1.3 Before Bouguer: The Tractrix 23 1.4 The Myth of Leonardo da Vinci 27 1.5 Apollonius Pursuit and Ramchundra's Intercept Problem 29 Chapter 2: Pursuit of (Mostly) Maneuvering Targets 41 2.1 Hathaway's Dog-and-Duck Circular Pursuit Problem 41 2.2 Computer Solution of Hathaway's Pursuit Problem 52 2.3 Velocity and Acceleration Calculations for a Moving Body 64 2.4 Houghton's Problem: A Circular Pursuit That Is Solvable in Closed Form 78 2.5 Pursuit of Invisible Targets 85 2.6 Proportional Navigation 93 Chapter 3: Cyclic Pursuit 106 3.1 A Brief History of the n-Bug Problem, and Why It Is of Practical Interest 106 3.2 The Symmetrical n-Bug Problem 110 3.3 Morley's Nonsymmetrical 3-Bug Problem 116 Chapter 4: Seven Classic Evasion Problems 128 4.1 The Lady-in-the-Lake Problem 128 4.2 Isaacs's Guarding-the-Target Problem 138 4.3 The Hiding Path Problem 143 4.4 The Hidden Object Problem: Pursuit and Evasion as a Simple Two-Person, Zero-Sum Game of Attack-and-Defend 156 4.5 The Discrete Search Game for a Stationary Evader -- Hunting for Hiding Submarines 168 4.6 A Discrete Search Game with a Mobile Evader -- Isaacs's Princess-and-Monster Problem 174 4.7 Rado's Lion-and-Man Problem and Besicovitch's Astonishing Solution 181 Appendix A: Solution to the Challenge Problems of Section 1.1 187 Appendix B: Solutions to the Challenge Problems of Section 1.2 190 Appendix C: Solution to the Challenge Problem of Section 1.5 198 Appendix D: Solution to the Challenge Problem of Section 2.2 202 Appendix E: Solution to the Challenge Problem of Section 2.3 209 Appendix F: Solution to the Challenge Problem of Section 2.5 214 Appendix G: Solution to the Challenge Problem of Section 3.2 217 Appendix H: Solution to the Challenge Problem of Section 4.3 219 Appendix I: Solution to the Challenge Problem of Section 4.4 222 Appendix J: Solution to the Challenge Problem of Section 4.7 224 Appendix K: Guelman's Proof 229 Notes 235 Bibliography 245 Acknowledgments 249 Index 251
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