The Brachistochrone Problem
The Brachistochrone problem is one of the most famous problems in the history of mathematics and was posed by
the Swiss mathematician John Bernoulli in 1696 as a challenge ''to the most acute mathematicians of the entire world''. The problem can be stated as follows:
Given two points on a plane at different heights, what is the shape of the wire down which a bead will slide (without friction) under the influence of gravity so as to pass from the upper point to the lower point in the shortest amount of time?