This is analagous to one of the quirks of each geometry in hyperbolic geometry the sum of the angles of a triangle is greater than 180 degrees, while Euclidean has the sum of a triangles angles to be 180 degrees exactly.
According to current theories in the field of cosmology, if the geometry is hyperbolic, the universe will expand indefinitely if the geometry is Euclidean, the universe will expand indefinitely at escape velocity and if the geometry is elliptic, the expansion of the universe will coast to a halt, and then the universe will start to shrink, possibly to explode again. 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. Most cosmologists believe that knowing which geometry is the most correct is important. 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. At the present time mathematicians are still not sure which of the three geometries provides the best representation of the entire universe. 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. 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. Both of those geometries hold up to a two dimensional world, as well as the third dimension.Ĭosmology - Cosmology is the study of the origin, constitution, structure, and evolution of the universe. It has been argued that Euclidean Geometry, while good for architecture and to survey land, when it is moved into the third dimension, the postulates do not hold up as well as those of hyperbolical and spherical geometry. The one problem that some find with it is that it is not accurate enough to represent the three dimensional universe that we live in. it has remained remarkably correct and accurate to real world situations faced on Earth. Since Euclid first published his book Elements in 300 B.C. The Applications Of Non-Euclidean Geometry
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