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. Referenced
on Wolfram|Alpha Developable Surface
Cite this as:
Weisstein, Eric W. "Developable Surface."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/DevelopableSurface.html

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