Minimal path between two points via a line

There is a unique shortest path from AA to BB reflecting in the line LL. It is seen in the diagram that the angles of incidence and reflection (α\alpha and β\beta) are equal for this shortest path. The variational priciple here gives the well-known law for the reflection of light (and billiard balls!).

It was known to the Greek mathematician Heron of the first Century AD and it appears as a problem in his book Catoptrica.