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Development (differential geometry)
In classical differential geometry, development refers to the simple idea of rolling one smooth surface over another in Euclidean space. For example, the tangent plane to a surface (such as the sphere or the cylinder) at a point can be rolled around the surface to obtain the tangent plane at other points.
==Properties==
The tangential contact between the surfaces being rolled over one another provides a relation between points on the two surfaces. If this relation is (perhaps only in a local sense) a bijection between the surfaces, then the two surfaces are said to be developable on each other or ''developments'' of each other. Differently put, the correspondence provides an isometry, locally, between the two surfaces.
In particular, if one of the surfaces is a plane, then the other is called a developable surface: thus a developable surface is one which is locally isometric to a plane. The cylinder is developable, but the sphere is not.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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