Cycloid

Demonstration of the properties of the evolute of a cycloid

The length of the cycloid as consequence of the property of its evolute

A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a roulette, a curve generated by a curve rolling on another curve.

The inverted cycloid (a cycloid rotated through 180°) is the solution to the brachistochrone problem (i.e., it is the curve of fastest descent under gravity) and the related tautochrone problem (i.e., the period of an object in descent without friction inside this curve does not depend on the object's starting position).

单词	Curate cycloid
释义	Curate cycloid 英语百科 Cycloid A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a roulette, a curve generated by a curve rolling on another curve. The inverted cycloid (a cycloid rotated through 180°) is the solution to the brachistochrone problem (i.e., it is the curve of fastest descent under gravity) and the related tautochrone problem (i.e., the period of an object in descent without friction inside this curve does not depend on the object's starting position).
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Curate cycloid

Cycloid