 Of course, one can make experiments using large triangles and measuring the angles, as Lobachevskii, Riemann and others had suggested. To maximize dimensions, assume that the sides of the triangle are made by rays of light. Now, suppose that within the limits of experimental error the result of the experiment is that the angle sum of the triangle is less that \(\pi\), a result consistent with non-Euclidean geometry but inconsistent with Euclidean geometry. The only conclusion one can draw, said Poincaré, is that either light rays travel along straight lines and space is non-Euclidean, or that space is Euclidean and light rays travel along curves.