A developable surface is a ruled surface having Gaussian curvature everywhere. Developable surfaces therefore include the cone, cylinder, elliptic cone, hyperbolic cylinder, and plane.

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.

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.

CITE THIS AS:

Weisstein, Eric W. "Developable Surface." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DevelopableSurface.html