Brachistochrone curve

Fastest curve descent without friction
Abstract

In physics and mathematics, a brachistochrone curve, or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides frictionlessly under the influence of a uniform gravitational field to a given end point in the shortest time. The problem was posed by Johann Bernoulli in 1696 and famously solved in one night by Isaac Newton in 1697, though Bernoulli and several others had already found solutions of their own months earlier.

Wikipedia