Mathematicians Challenge 150-Year-Old Geometry Rule with New Discovery
Mathematicians from the Technical University of Munich, the Technical University of Berlin, and North Carolina State University have discovered a counterexample to a long-standing principle in geometry. The principle, originating from French mathematician Pierre Ossian Bonnet, posits that the metric and mean curvature of a compact surface can determine its exact shape. The researchers constructed two torus-shaped surfaces that share identical metric and mean curvature values but differ in overall structure. This finding challenges the assumption that these properties alone can define a surface's shape, providing the first explicit example of this phenomenon. 
