entwickelbaren

Entwickelbaren is the declined plural form of the German adjective entwickelbar, meaning "developable" or "able to be developed/unfolded." In use, it appears as a modifier for objects or properties that can be developed, unfolded or unrolled under certain constraints. The term is common in mathematics and geometry, as well as in technical disciplines dealing with sheet materials or surfaces.

In geometry, developable surfaces are those that can be flattened onto a plane without distortion (no stretching or tearing). This is equivalent to having zero Gaussian curvature almost everywhere. Classical examples are planes, right circular cones and right circular cylinders. Developable surfaces are often described as ruled surfaces, since they can be generated by moving a straight line along a curve.

Applications of developable surfaces occur in fields such as sheet metal fabrication, architecture, textile design and computer graphics. In sheet metal and manufacturing, using developable surfaces allows products to be formed from flat sheets with minimal distortion. In architecture and design, developable panels enable curved forms to be assembled from flat components. In computer graphics and geometric modeling, developability constraints help in texture mapping and mesh processing when preserving metric properties is important.

Notes on usage: entwickelbaren serves as the plural, declined form in phrases like die entwickelbaren Flächen or mit den entwickelbaren Strukturen. The related noun form is Entwickelbarkeit (developability). In English, the corresponding term is developable.