Tautochrone Curve
A tautochrone or isochrone curve (from Greek prefixes tauto- meaning same or iso- equal, and chrono time) 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 curve is a cycloid, and the time is equal to π times the square root of the radius over the acceleration of gravity.
Read more about Tautochrone Curve: The Tautochrone Problem, Lagrangian Solution, "Virtual Gravity" Solution, Abel's Solution
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