Bonnet's theorem

Bonnet's theorem states that in a geometry that follows certain mathematical rules, if a surface has a specific kind of curvature, then it can be uniquely determined by its properties at a small area. This means that small, localized measurements or observations of curvature can reveal the overall shape and structure of the entire surface. Essentially, it highlights the deep connection between local geometric properties and the global structure of surfaces, such as in the study of shapes in mathematics and physics.