Sutton's theorem

Sutton's theorem states that for a convex shape, the shortest total length of a network of straight lines connecting multiple points inside it (a Steiner minimal tree) is always longer than the sum of the shortest paths connecting those points along the shape's boundary (like walking around the shape). In simple terms, connecting points inside a shape directly with the shortest possible network always costs more than just following the shape's outline to connect the same points. This helps understand how to design efficient networks or connections within bounded areas.