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. '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. 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. '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. The developable surfaces which can be realized in three-dimensional space include: 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.