 In his study of formal systems for geometry (Hempel 1945b), Hempel discusses the existence of alternatives based upon different axioms, which differentiate Euclidean geometry from its non-Euclidean rivals. According to Euclid, for example, the sum of the interior angles of a triangle must equal 180° and, in relation to a point separate from a given line, one and only one parallel line passes through it. The alternatives advanced by Lobachevsky (hyperbolic) and by Riemann (elliptical), however, which represent the surface of a sphere and of a saddle, respectively, violate both of those conditions, albeit in different ways. Hempel emphasized that all three, as formal systems, are on a par, where the most appropriate choice to describe the geometry of space depends on the outcome of empirical studies. As it happened, Einstein would adopt a generalized form of Riemannian geometry in his general theory of relativity.