Developable surface
A developable surface is a surface that can be flattened onto a plane without distortion (i.e. stretching, compressing, tearing). Inversely, it is a surface that can be made by transforming a plane (i.e. folding, bending, rolling). Basic examples of developable surfaces are cones and cylinders. Spheres are not developable surfaces as they cannot be unrolled into a plane.
Formally, in mathematics, a developable surface is a surface with zero Gaussian curvature; that is, for every point on the surface, there is a straight line on the surface that passes through that point. This is also known as being linear in one direction. A plane is linear in all directions; a cylinder is linear in one and curved in the other; a sphere is curved in two directions.
Because a developable surface is linear in one direction, it can be visualised as the surfaced formed by moving a straight line in space. For example, a cone is formed by keeping one end of a line fixed while moving the other end in a circle. More complex developable surfaces may be formed by an intersection of sub-surfaces (formed by moving different lines).
Developable surfaces are important for various applications. They are intrinsic to cartography as they relate to map projections. They are also important in manufacturing objects from sheet metal, cardboard, etc.