Chases and Escapes: The Mathematics of Pursuit and Evasion

We all played tag when we were kids. The rules couldn't be easier--one player is designated "it" and must try to tag out one of the others. 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 at play in military strategy, high-seas chases by the Coast Guard, even romantic pursuits. In Chases and Escapes, Paul Nahin gives us the first complete history of this fascinating area of mathematics.Writing in an accessible style that has been enjoyed by popular-math enthusiasts everywhere, Nahin traces the development of modern pursuit theory from its classical analytical beginnings to the present day. Along the way, he informs his mathematical discussions with fun facts and captivating stories. Nahin invites readers to explore the different approaches to solving various chase-and-escape problems. He draws upon game theory, geometry, linear algebra, target-tracking algorithms--and much more. Nahin offers an array of challenging puzzles for beginners on up, providing historical background for each problem and explaining how each one can be applied more broadly. Chases and Escapes includes solutions to all problems and provides computer programs that readers can use for their own cutting-edge analysis.This informative and entertaining book is the first comprehensive treatment of the subject, one that is sure to appeal to anyone interested in the mathematics that underlie the all-too-human endeavor of pursuit and evasion.