Theorema Egregium

Theorema Egregium, discovered by mathematician Carl Friedrich Gauss, states that certain properties of a surface, such as curvature, remain unchanged even when the surface is bent or stretched, as long as it is not torn or glued. This means that the intrinsic geometry of a shape—how it curves and bends—doesn't depend on how it is presented in space. For example, while a flat piece of paper can be curled into a cylinder, its essential flatness doesn’t change. This concept is fundamental in understanding the geometry of surfaces in mathematics and physics.