A cycloid is the curve defined by the path of a point on the edge of circular wheel as the wheel rolls along a straight line. It is an example of a roulette, a curve generated by a curve rolling on another curve.
graph of z=x²-y²
Demonstration of the divided 12hr clock face, into 12 individuals created into one still image, with motion of time.
A ray through the origin intercepts the hyperbola in the point , where is twice the area between the ray and the x-axis. For points on the hyperbola below the x-axis, the area is considered negative.