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 generated by a curve rolling on another curve.
Cycloidal arches at the Kimbell Art Museum
In mathematics, a curve is an object similar to a line, but that does not have to be straight.
Megalithic art from Newgrange showing an early interest in curves
A dragon curve with a positive area