Tangent developable

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The tangent developable of a helix

The tangent developable of a space curve $γ(t)$ is a ruled surface of the form $\gamma(t)+s \gamma^\prime(t)$ . Intuitively it is the union of the tangent lines to the 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.