A developable surface, also called a flat surface (Gray
et al. 2006, p. 437), is a ruled surface having Gaussian
everywhere. Developable surfaces therefore include the cone,
cylinder, elliptic cone,
hyperbolic cylinder, and plane.
Other examples include the tangent developable,
generalized cone, and generalized
regular surface is developable iff its Gaussian curvature vanishes identically
(Gray et al. 2006, p. 398).
A developable surface has the property that it can be made out of sheet metal, since such a surface must be obtainable by transformation from a plane (which has
curvature 0) and every point on such a surface lies on at least one straight
See also Binormal Developable
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References Gray, A.; Abbena, E.; and Salamon, S. Boca
Raton, FL: CRC Press, pp. 398 and 437-438, 2006. Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd ed. Kuhnel, W. Providence, RI: Amer. Math. Soc., 2002. Differential
Geometry Curves--Surfaces--Manifolds. Snyder,
J. P. U. S. Geological Survey Professional
Paper 1395. Washington, DC: U. S. Government Printing Office, p. 5, 1987. Map
Projections--A Working Manual. Referenced
on Wolfram|Alpha Developable Surface
Cite this as:
Weisstein, Eric W. "Developable Surface."
From --A Wolfram Web Resource. MathWorld https://mathworld.wolfram.com/DevelopableSurface.html