Department of Physics and Materials Science

Brachistochrone

What’s the fastest path between two points?

The Brachistochrone ("shortest-time") curve is the curve for which an object rolls between two endpoints in the shortest possible time. Interestingly, it is not the shortest curve between the two points, a straight line. ​

In 1696, Johann Bernoulli challenged his contemporaries to find the brachistochrone curve. It was found to be a cycloid, the curve generated by a point on a rolling wheel (Figure b).​

Curve B is a segment of a cycloid, so the ball rolling down it wins the race (though Curve A is a close second!)​

The brachistochrone problem led to the development of the Calculus of Variations, a method used to solve countless problems in physics and  engineering, like finding the path by light through any medium, or determining the shape of a soap bubble with any given border (Figure c).​

This demonstration is currently displayed in the Hallway on the 2nd Floor in Manning Hall.

See also Tautochrone.