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In mathematics, a developable surface is a smooth surface with zero Gaussian curvature. That is, it is a surface that can be flattened onto a plane without distortion. Conversely, it is a surface which can be made by transforming a plane. In three dimensions all developable surfaces are ruled surfaces. There are developable surfaces in four-dimensional space R 4 {\displaystyle \mathbb {R} ^{4}} which are not ruled.
The envelope of a single parameter family of planes is called a developable surface.
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