Both of those geometries hold up to a two dimensional world, as well as the third dimension. The recognition of the existence of the non-Euclidean geometries as mathematical systems was resisted by many people who proclaimed that Euclidean geometry was the one and only geometry. To try and 'validate' the geometries to Euclid believers the truth of the geometry was presented in the sense of better representing our universe, through observation. At the present time mathematicians are still not sure which of the three geometries provides the best representation of the entire universe. While Euclidean geometry provides an excellent representation for the part of the universe that we inhabit, like Newton's Laws of physics, they break down when placed in situations that their originators could not have imagined.
Most cosmologists believe that knowing which geometry is the most correct is important.
This stems from the belief that the future of the universe is expected to be determined by whatever is the actual geometry of the universe. Elliptic geometry has the sum of the angles of a triangle to be less than 180 degrees. Back To Top The Theory of General Relativity Einstein's Theory Of General Relativity is based on a theory that space is curved. The cause is explained by the theory itself. The distortions of space affect the motions of matter and energy.