Chases and Escapes: The Mathematics of Pursuit and Evasion

By Paul J. Nahin | Go to book overview

Chapter 2
Pursuit of (Mostly)
Maneuvering
Targets

2.1 Hathaway’s Dog-and-Duck Circular Pursuit Problem

In chapter 1 we considered only the case of the pursued (the chased one, the fugitive, the evader, the escaper, the target, etc.) as always moving along a straight path. It didn’t take very long after Bouguer’s original 1732 statement of the pursuit problem, however, for analysts to begin to consider more complicated evasion paths (what Bouguer called the ligne de fuite). The simplest such flight or fleeing path (in terms of shape) would, for most people, be a circular path, and one finds such paths being discussed as early as 1742. These early extensions of the pursuit problem statement (but not the solution) first appeared in a curious journal, published once a year from 1704 to 1841, called the Ladies’ Diary. Published in England, the journal was quite popular, with a subscription list of several thousand, and almost surely this was because it devoted a large fraction of its space to intriguing mathematical puzzles. These puzzles were not trivial — here’s one from

-41-

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