Curve generated by a point of a circle's circumference rolling on a plane. The cycloid posses interesting physical properties. It is brachistochronous and tautochronous: brachistochronous, because it represents the path completed in the shortest time between two points for a given type of motion (such as a fall under the effect of gravity); tautochronous, because a body made to oscillate along a cycloid will always take the same time to cover it, whatever the amplitude of the oscillation. Galileo (1564-1642) mistakenly believed circular oscillations to be tautochronous. The brachistochronous property of the cycloid was demonstrated by Jacques Bernoulli (1654-1705) in 1697, while Christiaan Huygens (1629-1695) proved its tautochronism in 1659.

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