The curtate variety of this figure contains a fixed point on its inside, which contrasts with its prolate variety. Huygens used its isochronous properties to design the first 
The curtate variety of this figure contains a fixed point on its inside, which contrasts with its prolate variety. Huygens used its isochronous properties to design the first pendulum clock guaranteeing regular swing independent of pendulum height. This figure is represented parametrically by the equations x equals r times the quantity one minus sine of t, and y equals r times the quantity one minus cosine of t. It provides the solution to the problem of finding the curve of fastest descent, also known as the brachistochrone problem. For 10 points, name this figure traced out by a point on a rolling circle.
The curtate variety of this figure contains a fixed point on its inside, which contrasts with its prolate variety.
cycloid 