The first problem of this type (calculus of variations) that mathematicians solved was that of the brachistochrone, or the curve of fastest descent, which Johann Bernoulli proposed in 1696. The problem was posed 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? Severalwell-known mathematicians, including Issac Newton, provided solutions. Using the method of calculus of variations, show that the solution is a cycloid x = (t − sin t)

and y = (1 − cos t) where  is a constant and t is a parameter.