Chases and Escapes

Preface to the Paperback Edition xiii

What You Need to Know to Read This Book (and How I Learned What I Needed to Know to Write It) xxvii

Introduction 1

Chapter 1. The Classic Pursuit Problem 7

- 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