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 generated by a curve rolling on another curve.
The cycloid, with the cusps pointing upward, is the curve of fastest descent under constant gravity (the brachistochrone curve). It is also the form of a curve for which the 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).
My uncle Toby understood the nature of a parabola as well as any man in England—but was not quite such a master of the cycloid;——he talked however about it every day——the bridge went not forwards.
Laurence Sterne. The Life and Opinions of Tristram Shandy, Gentleman (1759)
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In the first course, there was a shoulder of mutton cut into an equilateral triangle, a piece of beef into a rhomboides, and a pudding into a cycloid.