Fermat's principle, Huygens' principle, Hamilton's optics and sailing strategy

Abstract

Fermat's principle asserts that light takes the path of minimum (actually extremal) time. Sailors often wish to find paths of minimum time. Thus by thinking of a sailboat as a light ray, a sailor can use Fermat's principle to describe the optimum sailing strategy. Huygens' principle and Hamiltonian optics follow from Fermat's principle, so a sailor can use Huygens' principle to visualize least-time paths, and Hamilton's optics provides a mathematical description of these paths. In especially simple cases, the optics-based formalism can be used to describe and quantify the basic tactics of sailboat racing.