A transcendental curve, its main application being that it could be used to trisect a general angle, an impossible construction with ruler and compass. In the figure, if the radius OA rotates uniformly to radius OB and at the same rate the line CD moves from the top to the base, then when the radius has reached OP we can define the point P’ as the intersection of CD with OP. The quadratrix is the curve traced by P’. The angle OP could then be trisected by constructing C’D’ at one-third the height of OC, and if C’D’ meets the quadratrix at P’’, then OP’’ trisects OP.

A quadratrix

The quadratrix can be parameterized as

where a>0.