Brachistochrone Problem -- From Wolfram MathWorld - mathworld.wolfram.com  ## Metadata - Author: **mathworld.wolfram.com** - Full Title: Brachistochrone Problem -- From Wolfram MathWorld - Category: #articles - Tags: #mathematic - URL: https://mathworld.wolfram.com/BrachistochroneProblem.html#:~:text=The%20brachistochrone%20problem,and%20Robbins%201996). ## Highlights - 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).