The Cissoid

Introduction:

The cissoid was first studied by the Greek mathematician Diocles, in connection with the problems of doubling a cube and trisecting an angle.

Definition:

Implicitly, it is defined by

Geometrically, the cissoid is formed by taking the set of points P traces as the line AR moves so that the distance from A to P is the same as the distance from Q to R.

Properties:

Velocity and Acceleration:

The Tangent Vector:

Arc Length:

Curvature: