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Tautochrone

Not all ramps are created equal​!

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. ​

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.​

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).​

See also Brachistocrone.​