Developable Surface (original) (raw)
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A developable surface, also called a flat surface (Gray et al. 2006, p. 437), is a ruled surface having Gaussian curvature 
everywhere. Developable surfaces therefore include the cone,cylinder, elliptic cone,hyperbolic cylinder, and plane. Other examples include the tangent developable,generalized cone, and generalized cylinder.
A 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 Gaussian curvature 0) and every point on such a surface lies on at least one straight line.
See also
Binormal Developable, Gaussian Curvature, Normal Developable, Ruled Surface, Synclastic,Tangent Developable
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References
Gray, A.; Abbena, E.; and Salamon, S. Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd ed. Boca Raton, FL: CRC Press, pp. 398 and 437-438, 2006.Kuhnel, W. Differential Geometry Curves--Surfaces--Manifolds. Providence, RI: Amer. Math. Soc., 2002.Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, p. 5, 1987.
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Cite this as:
Weisstein, Eric W. "Developable Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DevelopableSurface.html