|
In mathematics, a developable surface (or torse: archaic) is a surface with zero Gaussian curvature. That is, it is a surface that can be flattened onto a plane without distortion (i.e. "stretching" or "compressing"). 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 R4 which are not ruled. ==Particulars== The developable surfaces which can be realized in three-dimensional space include: *Cylinders and, more generally, the "generalized" cylinder; its cross-section may be any smooth curve *Cones and, more generally, conical surfaces; away from the apex * The oloid and the sphericon are members of a special family of solids that develop their entire surface when rolling down a flat plane. * Planes (trivially); which may be viewed as a cylinder whose cross-section is a line *Tangent developable surfaces; which are constructed by extending the tangent lines of a spatial curve. * The torus has a metric under which it is developable, which can be embedded into three-dimensional space by the Nash embedding theorem〔.〕 and has a simple representation in four dimensions as the Cartesian product of two circles: see Clifford torus. Formally, in mathematics, a developable surface is a surface with zero Gaussian curvature. One consequence of this is that all "developable" surfaces embedded in 3D-space are ruled surfaces (though hyperboloids are examples of ruled surfaces which are not developable). Because of this, many developable surfaces can be visualised as the surface formed by moving a straight line in space. For example, a cone is formed by keeping one end-point of a line fixed whilst moving the other end-point in a circle. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「developable surface」の詳細全文を読む スポンサード リンク
|