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“tautochrone”

tautochrone

That curve upon which a particle moving under the action of gravity (or any given force) will reach the lowest (or some fixed) point in the same time, from whatever point it starts.

A tautochrone or *isochrone* curve is the curve for which the time taken by a frictionless particle sliding down it under uniform gravity to its lowest point is independent of its starting point. The curve is a cycloid, and the time is equal to π times the square root of the radius over the acceleration of gravity.