beetle problem | bug problem | four-bug problem | four dog problem | three dogs problem

In the mice problem, also called the beetle problem, n mice start at the corners of a regular n-gon of unit side length, each heading towards its closest neighboring mouse in a counterclockwise direction at constant speed. The mice each trace out a logarithmic spiral, meet in the center of the polygon, and travel a distance d_n = 1/(1 - cos((2π)/n)).

Apollonius pursuit problem | Brocard points | pursuit curve | spiral | tractrix | whirl

mice