Brachistochrone curve
In physics and mathematics, a brachistochrone 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. The curve of fastest descent is not a straight (yellow) or polygonal line (green) but a cycloid (red).