The Epispiral

Introduction:

The epispiral has n branches when n is odd, each of which has two asymptotes (shown above). If n is even, the spiral will have 2n branches.

Definition:

In polar coordinates, the epispiral is defined by

Properties:

Velocity and Acceleration:

a[t] = [click for formula]

The Tangent Vector:

Arc Length:

Curvature: