Developable Surface

A developable surface, also called a flat surface (Gray et al. 2006, p. 437), is a ruled surface having Gaussian curvature K=0 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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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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Developable Surface

Cite this as:

Weisstein, Eric W. "Developable Surface." From MathWorld--A Wolfram Web Resource.

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