The

**brachistochrone** (least-time) problem may be familiar if you have completed the first two years of the standard Calculus curriculum for science and mathematics students.

The problem is:

In mathematics and physics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos), meaning "shortest time"), or curve of fastest descent, is the one lying on 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. Incidentally, for a given starting point, the brachistochrone curve is the same as the tautochrone curve. More specifically, the solution to the brachistochrone and tautochrone problem are one and the same, the cycloid.

Put another way, what is the shape of a ramp which allows for the fastest travel time.

For geometry fans this video by Michael Stevens and Adam Savage will be satisfying.

Vsauce:

https://www.youtube.com/watch?v=skvnj67YGmw
Edited 9/20/2017 01:01:27