On June 1696, Johann Bernoulli posted a mathematic problem to the readers of Acta Eruditorum which was called the brachistochrone (“shortest time” in ancient Greek). His problem statement was as follows: “Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and reaches B in the shortest time”.
A similar problem was earlier attempted to be solved by Galileo in 1638 without success. Isaac Newton managed to solve the problem as well as Johann’s brother Jakob Bernoulli as this question that seems relatively simple required an advanced understanding of physics, calculus and Newton’s own minimal resistance problem.
The Image above indicates the original design (top) and the new design (bottom) which incorporates a cycloid curve.