 There are properties of the space that are independent of the coordinate system. If two different coordinate systems give out different coordinates, but in such a way that the distance between the points is preserved, then either system gives us the same geometry, and we find that the two agree on the curvatures at each point, on distances, and so forth. Yet the framework of differential geometry proposed by Riemann is very flexible and general. He found that it allowed not only for alternatives to Euclidean geometry, but even for geometries where the generalized curvature does change from point to point. Initially this was scarcely taken up, and most authors focused on geometries of constant curvature. As Riemann explained, his framework allowed for geometries of negative curvature (this is the Lobachevskii-Bolyai case), of positive curvature (a new kind, often called elliptic geometry, or ‘Riemannian’ in a narrow sense), and also of zero curvature (Euclidean).