Stephenson:Neal:The System of the World:139:Brachistochrone Problem

From the Quicksilver Metaweb.

Brachistochrone Problem

A challenge posed in 1696 by the Bernoulli's during the Priority Dispute over the invention of the Calculus. Briefly, the problem is to find the curve between two points such that a particle travelling along that curve under the influence of gravity and free from friction will move from point A to point B in the minimum amount of time.

More information, including a detailed solution, may be found at Mathworld's article on the problem.