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
Cycloidal arches at the Kimbell Art Museum
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
Cycloid
…period of an object in simple harmonic motion (rolling up and down repetitively) along the curve does not depend on the object's starting position (the tautochrone curve). In physics, when a charged particle at rest is put under uniform electric and magnetic fields perpendicular to one another, the particle’s trajectory…
Christiaan Huygens, Horologium oscillatorium sive de motu pendulorum, 1673