As we have previously discussed, it is by no means guaranteed that the space in which measurements are made in an economic system—or, indeed, in many complex physical systems—is EuclideanEuclidean space. The assumption of a flat, uniform background where standard calculus applies may fail when the structure of the system itself defines or modifies the space of measurement. Riemannian geometryRiemannian geometry offers the mathematical framework to go beyond this limitation. It allows us to define distances, angles, and curvature in spaces that are locally Euclidean but globally curved, structures known as manifoldsManifold.