- Tangential developable
In the mathematical study of the
differential geometry of surfaces , a tangential developable is a particular kind ofdevelopable surface obtained from acurve inEuclidean space as the surface swept out by thetangent line s to the curve. Such a surface is also the envelope of thetangent plane s to the curve.With the exceptions of the plane, a cylinder, and a cone, every developable surface in three-dimensional Euclidean space is the tangential developable of a certain curve, the edge of regression. This curve is obtained by first developing the surface into the plane, and then considering the image in the plane of the generators of the ruling on the surface. The envelope of this family of lines is a plane curve whose inverse image under the development is the edge of regression. Intuitively, it is a curve along which the surface needs to be folded during the process of developing into the plane.
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