The Twisted Cubic

Click for VRML

Introduction:

The twisted cubic is formed by taking a parabola in the xy plane and bending the ends in the z direction so that the shadow of the curve on the xz plane looks like a cubic. Note that, while the parameterization of the function is extremely simple, its arclength and Frenet frame are complicated.

Definition:

Properties:

Velocity and Acceleration:

The Frenet Frame:

Arc Length:

Curvature and Torsion: