# Metadata Source URL:: https://mathworld.wolfram.com/BrachistochroneProblem.html#:~:text=The%20brachistochrone%20problem,and%20Robbins%201996). Topics:: #mathematic --- # Brachistochrone Problem -- from Wolfram MathWorld ## Highlights > [!quote]+ Updated on 100922_161658 > > The brachistochrone problem was one of the earliest problems posed in the calculus of variations. Newton was challenged to solve the problem in 1696, and did so > the very next day (Boyer and Merzbach 1991, p. 405). In fact, the solution, > which is a segment of a cycloid, was found by Leibniz, > L'Hospital, Newton, and the two Bernoullis. Johann Bernoulli solved the problem using > the analogous one of considering the path of light refracted by transparent layers > of varying density (Mach 1893, Gardner 1984, Courant and Robbins 1996).