By no overestimation, the 1860s in Germany saw a revolution in geometry. Riemann's famous Habilitationsschrift and Helmholtz's mathematical treatment of differential geometry showed that the three-dimensional flat space of Euclid was but one of many possible spaces of constant curvature. These new spaces might have any number of dimensions, they might have various degrees of curvature (positive, zero, and negative), or they might be simple extended manifolds of place without the property of distance or measure.