Curvature of the universe
The curvature is a quantity describing how the geometry of a space differs locally from the one of the flat space . The curvature of any locally isotropic space (and hence of a locally isotropic universe) falls into one of the three following cases: Zero curvature (flat); a drawn triangle's angles add up to 180° and the Pythagorean theorem holds; such 3-dimensional space is locally modeled by Euclidean space E 3 .Positive curvature; a drawn triangle's angles add up to more than 180°; such 3-dimensional space is locally modeled by a region of a 3-sphere S 3 .Negative curvature; a drawn triangle's angles add up to less than 180°; such 3-dimensional space is locally modeled by a region of a hyperbolic space H 3 . Curved geometries are in the domain of Non-Euclidean geometry . An example of a positively curved space would be the surface of a sphere such as the Earth. A triangle drawn from th...