# Chases and Escapes: The Mathematics of Pursuit and Evasion

By Paul J. Nahin | Go to book overview

Chapter 3
Cyclic Pursuit

3.1 A Brief History of the n-Bug Problem, and Why It Is of Practical Interest

In the May 1877 issue of Nouvelle correspondance mathématique the French mathematician Edouard Lucas (1842-1891) formally posed the following pursuit problem, the first really new innovation in pursuit questions since Bouguer’s original problem:

Three dogs are placed at the vertices of an equilateral triangle;
they run one after the other. What is the curve described by each
of them?

The answer was not long in coming: in the August issue Henri Brocard (mentioned in the previous chapter) stated that, if we suppose the dogs to start at the same time and to run with the same speed, then the pursuit curve for each dog is a logarithmic spiral. In the next section we’ll go through the mathematics of Brocard’s answer, but for now I’ll limit myself to outlining how the problem itself evolved over time.

But even before I do that, if you read the opening to the previous paragraph again perhaps you’ll wonder why I emphasized the word formally when introducing Lucas’s problem. The reason is that the problem had actually appeared years earlier on the famous Cambridge University Mathematical Tripos Examination of January 1871. That

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