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    Chases and Escapes: The Mathematics of Pursuit and Evasion

    Chases and Escapes: The Mathematics of Pursuit and Evasion

    by Paul Nahin

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    (With a New preface by the author)
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    Customer Reviews

    Paul J. Nahin is the best-selling author of many popular math books, including Mrs. Perkins's Electric Quilt, Digital Dice, Dr. Euler's Fabulous Formula, When Least Is Best, and An Imaginary Tale (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.

    Table of Contents

    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

    What People are Saying About This

    Desmond Higham

    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

    Arthur Benjamin

    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

    Nick Hobson

    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"

    Martin Gardner

    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.

    Burton

    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

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    Want a NOOK? Explore Now

    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 also offers an array of challenging puzzles with their historical background and broader applications. Chases and Escapes includes solutions to all problems and provides computer programs that readers can use for their own cutting-edge analysis.


    Now with a gripping new preface on how the Enola Gay escaped the shock wave from the atomic bomb dropped on Hiroshima, this book will appeal to anyone interested in the mathematics that underlie pursuit and evasion.

    Some images inside the book are unavailable due to digital copyright restrictions.

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    Mathematics Teacher
    This book contains a well-written, well-organized collection of solutions to twenty-one challenging calculus and differential equation problems that concern pursuit and evasion as well as the historical background of each problem type.
    MAA Review
    This is a highly readable book that offers several colorful applications of differential equations and good examples of non-trivial integrals for calculus students. It would be a good source of examples for the classroom and or a starting point for an independent project.
    — Bill Satzer
    New Scientist
    In the 18th century, mathematicians began to tease apart how best to track down and intercept prey, inspired by pirate ships bearing down on merchant vessels. The mathematics is by no means trivial, and quickly becomes fiendish if the merchant ship takes evasive action. This is just one of the colorful problems in Paul Nahin's fascinating history of the mathematics of pursuit, in which he guides us masterfully through the maths itself—think lions and Christians, submarines and torpedoes, and the curvaceous flight of fighter aircraft.
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