**Tautochrone curves**

Drop a ball on this curve and it'll reach the bottom in the same amount of time, no matter where you drop it.

A

**tautochrone**is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point. The time is equal to π times the square root of the radius over the acceleration of gravity.

wikipedia.org/wiki/Tautochrone #math #physics