Differential geometry of surfaces | Surfaces | Differential geometry

Developable surface

In mathematics, a developable surface (or torse: archaic) is a smooth surface with zero Gaussian curvature. That is, it is a surface that can be flattened onto a plane without distortion (i.e. it can be bent without stretching or compression). Conversely, it is a surface which can be made by transforming a plane (i.e. "folding", "bending", "rolling", "cutting" and/or "gluing"). In three dimensions all developable surfaces are ruled surfaces (but not vice versa). There are developable surfaces in four-dimensional space which are not ruled. The envelope of a single parameter family of planes is called a developable surface. (Wikipedia).

Developable surface
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Related pages

Development (differential geometry) | Cross section (geometry) | Rolling | Helicoid | Tangent developable | Surface (mathematics) | Flatness (mathematics) | Three-dimensional space | Curve | Oloid | Torus | Point (geometry) | Mathematics | Sphere | Clifford torus | Apex (geometry) | Sphericon | Envelope (mathematics) | Ruled surface | Developable roller | Metric tensor | Conical surface | Hyperboloid | Gaussian curvature | Circle | Four-dimensional space | Tangent