BRACHISTOCHRONE

Brachistochrone (curve of fastest descent) the planar curve on which a body subjected only to the force of gravity will slide (without friction) between two points in the least possible time (see Figure). Finding the curve was a problem first posed by Galileo. In the late 17th century the Swiss mathematician Jakob Bernoulli offered a reward for the solution of this problem. He and his younger brother Johann, along with Gottfried Wilhelm Leibniz, Isaac Newton, and others, found the curve to be a cycloid (q.v.). See also isoperimetric problem.