Principle of least time, 2

Principle of least action, 4

Indeed Fermat’s principle does not hold standing alone, we now know it can be derived from earlier principles such as Huygens’ principle. Historically, Fermat’s principle has served as a guiding principle in the formulation of physical laws with the use of variational calculus (see Principle of least action).

— Wikipedia on Fermat’s principle

Fermat’s principle is very similar to the principle of least action but the derivation of Fermat’s principle from the principle of least action is less straightforward than you might think.

— Lubos Motl

2011.10.26 Wednesday ACHK