Probing the Geometry of Space - Mathematics circa 1900

Abstract

One of the most hotly debated topics of the late nineteenth century concerned the geometry of physical space, an issue that arose with the discovery of non-Euclidean geometries. Lobachevsky and Bolyai opened the way, but it was not until the 1860s that scientists began to take this revolutionary theory seriously. Assuming the free mobility of rigid bodies, Helmholtz concluded that the geometry of space was Euclidean or else of constant curvature (either positive of negative). In 1899 these cases were tested by the astronomer Karl Schwarzschild who used data on stellar parallax to estimate the minimum size of the universe. Many argued that the notion of a curved space was nonsensical, whereas Poincaré, the most prominent mathematician of the era, thought that the geometry of space could never be determined absolutely. These classical debates played a major role in the discussions spawned by Einstein’s general theory of relativity. David Rowe, geometry, space-mathematics, Euclid, Carl Friedrich Gauss, Gaussian curvature, Gaussian Theory, Einstein, differential geometry, playfair, spherical triangles, platonic solids, Netwon, non-Euclidean geometry, Riemann, Ricci, Poincare, Klein