Chases and Escapes : The Mathematics of Pursuit and Evasion

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. 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) Introduction Chapter 1. The Classic Pursuit Problem Chapter 2. Pursuit of (Mostly) Maneuvering Targets Chapter 3. Cyclic Pursuit Chapter 4. Seven Classic Evasion Problems 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 2.2 Appendix 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 Biographical note: NahinPaul J.: 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