Gauss and Poincar.C3.A9 Space

carl friedrich gauss



henri poincaré

although there prevailing kantian consensus @ time, once non-euclidean geometries had been formalised, began wonder whether or not physical space curved. carl friedrich gauss, german mathematician, first consider empirical investigation of geometrical structure of space. thought of making test of sum of angles of enormous stellar triangle, , there reports carried out test, on small scale, triangulating mountain tops in germany.

henri poincaré, french mathematician , physicist of late 19th century, introduced important insight in attempted demonstrate futility of attempt discover geometry applies space experiment. considered predicament face scientists if confined surface of imaginary large sphere particular properties, known sphere-world. in world, temperature taken vary in such way objects expand , contract in similar proportions in different places on sphere. suitable falloff in temperature, if scientists try use measuring rods determine sum of angles in triangle, can deceived thinking inhabit plane, rather spherical surface. in fact, scientists cannot in principle determine whether inhabit plane or sphere and, poincaré argued, same true debate on whether real space euclidean or not. him, geometry used describe space matter of convention. since euclidean geometry simpler non-euclidean geometry, assumed former used describe true geometry of world.