# Developable surface

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Related to Developable surface: ruled surface
 (Math.) a surface described by a moving right line, and such that consecutive positions of the generator intersect each other. Hence, the surface can be developed into a plane.

Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.
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The fact that each segment of the flat concrete plate can only be bent in one direction requires discretization of the double-curved cupola into a sequence of developable surface strips.
In differential geometry (CADDEO; MONTALDO, 2001), (DIMITRIC, 1992), (LOUBEAU; ONICIUC, 2007), (O'NEILL, 1983) that under the assumption of sufficient differentiability, a developable surface is either a plane, conical surface, cylindrical surface or tangent surface of a curve or a composition of these types.
A tangent developable surface is a constant angle surface if and only if the generating curve is a helix.
The parallel surface S to a timelike (spacelike) non - developable surface surface S at distance [delta] = 1/2H, H a positive constant, is synclastic (respectively, anticlastic).
This new class of mechanisms, called 'developable mechanisms,' get their name from developable surfaces, or materials that can take on 3-D shapes from flat conformations without tearing or stretching, like a sheet of paper or metal.
Abdel-Baky and Al-Ghefari in [9] demonstrated some interesting ruled and developable surfaces as a surface pencil from a given asymptotic curve.
Finally, Chapter 7 is dedicated to various aspects of extrinsic geometry, such as Frenet formulas for curves, ruled and developable surfaces, the shape operator, principal curvatures and curvature lines, etc.

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