Curves58 of 113
Cycloid
Charles de Bovelles, 1501; named by Galileo
The path of a point on the rim of a wheel that rolls along a straight line without slipping. One arch is eight times the wheel’s radius long, and the area under it is three times the wheel’s. Turned over, with its cusps pointing up, it is the curve of fastest descent under gravity, the brachistochrone.
x = r(t - sin t), y = r(1 - cos t)
On mathcurve.com as Cycloïde