# Chases and Escapes: The Mathematics of Pursuit and Evasion

## Synopsis

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.

## Excerpt

How will you escape it?
— a character in Dostoevsky’s The Brothers
Karamazov asks the same question that the
crewmen of the B-29 Enola Gay must have
asked their pilot, concerning the shock wave
from the world’s first atomic-bomb drop

The appearance of the hardcover edition of this book in 2007 prompted numerous letters and e-mails from readers all around the world. That surprised me at first, but after a little thought I think I know what might have prompted that response. In the introduction I mention a number of “pursuit-and-evasion” movies—including Cornel Wilde’s 1966 The Naked Prey — that I think exactly catch the spirit in which I wrote, and the appearance of this book just after Mel Gibson’s remake of Prey (the 2006 Apocalypto) is what perhaps sparked the imaginations of readers. In any case, I was of course pleased to learn that the book was being read. Since writing this book I have learned some new things.

In February 2008 I received a very nice note from Steve Strogatz, professor of theoretical and applied mechanics at Cornell, commenting on the n-bug cyclic pursuit problem of chapter 3. In particular, he wrote to tell me of his generalization (done when he was in high school!) of Martin Gardner’s n = 4 analysis, to directly derive this book’s equation (3.2.7) on p. 115. The following year Steve included an expanded discussion of his note to me in his book The Calculus of Friendship (Princeton University Press 2009), and you can find it there on pp. 15–22.

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