A developable surface, also called a flat surface (Gray et al. 2006, p. 437), is a ruled surface having Gaussian
curvature 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. Kuhnel, W. Differential
Geometry Curves--Surfaces--Manifolds. Snyder,
J. P. Map
Projections--A Working Manual. Referenced
on Wolfram|Alpha Developable Surface
Cite this as:
Weisstein, Eric W. "Developable Surface."
From MathWorld https://mathworld.wolfram.com/DevelopableSurface.html
Subject classifications
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.
