Physics
Tautochrone
Not all ramps are created equal鈥�!
The Tautochrone ("same-time") curve is that for which the time an object takes to roll down it doesn't depend on the object's starting point. 鈥�
In 1659, Christiaan Huygens proved that the tautochrone curve is a cycloid (yes, the Brachistochrone curve!). The curves in this display are segments of a cycloid, so each ball reaches the bottom at the same time.鈥�
Huygens took advantage of this property of the cycloid to construct a clock whose pendulum takes the same time per swing regardless of its starting position (regular pendulums take longer for larger swings).鈥�
See also Brachistocrone.鈥�