The Limaçon

Introduction:

The limaçon was discovered by Étienne Pascal, who named it for the snail (limaçon in French). He was also the father of the famous mathematician Blaise Pascal. The limaçon has the cardioid as a special case, when the value of b in the definition below is twice the value of a.

Definition:

Implicitly, it is defined by

Properties:

Velocity and Acceleration:

The Tangent Vector:

Arc Length:

Curvature: