Bernoulli's light beam solution of the brachistochrone problem through the eyes of Hamilton (Q2878137)

In this well-written paper, the author discusses Johann Bernoulli's solution of the brachistochrone problem using a light beam in a medium consisting of infinitely many isotropic layers and Fermat's principle which says that the path of a light beam is always a brachistochrone. In the second part of the paper, the author illustrates Hamilton's calculus of variations using the brachistochrone problem. By means of Hamilton's 1828 approach, one rediscovers the cycloid in a way that reminds us of the way in which Kepler's laws follow from his mechanical principles.