Tautochrone curve
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A tautochrone curve or isochrone curve 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 on the cu
Christiaan Huygens, Horologium oscillatorium sive de motu pendulorum, 1673
Cycloid
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In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve
Tautochrone curve
…taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve. The curve is a cycloid, and the time is equal to π times the square root of the radius of the circle which generates the cycloid, divided by the square root of the acceleration…
Cycloidal arches at the Kimbell Art Museum