developable

Developable is an adjective meaning capable of being developed. In mathematics, a developable surface is one that can be flattened onto a plane without distortion. This means the surface is isometric to a plane and has zero Gaussian curvature at every point. Classic developable surfaces are planes, cylinders, and cones. When a flat sheet is bent or rolled into such shapes, no stretching is required; conversely, surfaces like spheres or most complex curved forms generally cannot be developed without distortion.

In practical terms, developable surfaces are important in manufacturing and design because flat sheets of metal, cardboard, glass, or fabric can be formed into curved shapes by bending alone. This property simplifies fabrication and reduces costs, since it avoids material stretching. Applications include sheet-metal enclosures, architectural shells, packaging, and various forms of fashion or industrial design. In computer graphics and geometric modeling, developability concepts help create and approximate smooth curved surfaces by assembling or approximating planes, cylinders, and cones.

In everyday language, developable describes something that can be developed or brought to fruition. The technical sense, however, is primarily used in geometry and manufacturing contexts to characterize surfaces that can be unfolded into a plane without distortion.