## Chases and Escapes: The Mathematics of Pursuit and Evasion"Nahin provides beautiful applications of calculus, differential equations, and game theory. If you are pursuing an enjoyable collection of mathematical problems and the stories behind them, then your search ends here."--Arthur Benjamin, Harvey Mudd College "I know of no better way to grasp the basic concepts of calculus than to study pursuit-and-escape problems. Paul Nahin has made a superb survey of the vast field of such problems, from Zeno's paradox of Achilles and the tortoise through the famous four bugs that once made the cover of "Scientific American." Not only does he make clear the required differential equations, but he traces each problem's colorful history. No book on the topic could be more definitive or a greater pleasure to read."--Martin Gardner ""Chases and Escapes" is a superb treatment of the solutions to a variety of pursuit-evasion problems, some classic and others more contemporary. The content is accessible to undergraduates in mathematics or the physical sciences, with lots of supporting detail included. The author's lively writing style makes for enjoyable reading."--David M. Burton, University of New Hampshire "This book is a treasure trove of puzzles and an enjoyable read. Nahin's aim is to assemble a varied collection of pursuit-and-evasion problems. Fully worked solutions, from first principles, are presented for each problem. Problems are carefully set in their historical context. I am not aware of another book that covers pursuit-and-evasion problems in anywhere near as much detail as is presented here."--Nick Hobson, creator of the award-winning Web site "Nick's Mathematical Puzzles" "This is a well-written and novel book that is comprehensively researched and enthusiastically presented. Nahin offers a very good mixture of elegant math and lively historical interludes. I wasn't aware the topic had such a rich history and wide scope."--Desmond Higham, University of Strathclyde |

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### Contents

Introduction | 1 |

The Classic Pursuit Problem | 7 |

12 A Modern Twist on Bouguer | 17 |

The Tractrix | 23 |

14 The Myth of Leonardo da Vinci | 27 |

15 Apollonius Pursuit and Ramchundras Intercept Problem | 29 |

Pursuit of Mostly Maneuvering Targets | 41 |

22 Computer Solution of Hathaways Pursuit Problem | 52 |

45 The Discrete Search Game for a Stationary Evader Hunting for Hiding Submarines | 168 |

46 A Discrete Search Game with a Mobile Evader Isaacss PrincessandMonster Problem | 174 |

47 Rados LionandMan Problem and Besicovitchs Astonishing Solution | 181 |

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 23 | 209 |

23 Velocity and Acceleration Calculations for a Moving Body | 64 |

A Circular Pursuit That Is Solvable in Closed Form | 78 |

25 Pursuit of Invisible Targets | 85 |

26 Proportional Navigation | 93 |

Cyclic Pursuit | 106 |

32 The Symmetrical nBug Problem | 110 |

33 Morleys Nonsymmetrical 3Bug Problem | 116 |

Seven Classic Evasian Problems | 128 |

42 Isaacss GuardingtheTarget Problem | 138 |

43 The Hiding Path Problem | 143 |

Pursuit and Evasion as a Simple TwoPerson ZeroSum Game of AttackandDefend | 156 |

Solution to the Challenge Problem of Section 25 | 214 |

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 |

245 | |

Acknowledgments | 249 |

251 | |