Tangent developable

The tangent developable of a helix

The tangent developable of a space curve $\gamma (t)$ is a ruled surface of the form $\gamma (t)+s\gamma ^{\prime }(t)$. Intuitively it is the union of the tangent lines to the space curve. A result of Euler states that most developable surfaces can be obtained as a tangent developable. The exceptions are generalised cones and cylinders and the plane.

References

Weisstein, Eric W. "Tangent Developable". MathWorld.