July 13, 2012
Euclidean postulate , Hyperbolic & Elliptic non - Euclidean geometries
In 1829, the famous Russian mathematician Lobachevsky published his first non – Euclidean geometry which is known as hyperbolic geometry. In 1854, the German mathematician Riemann published the second non – Euclidean geometry whose name is elliptic geometry. The contemporaries of Lobachevsky and Riemann never recognized these two geometries but unfortunately made flippant remarks on these two beautiful and ground breaking results. Einstein emerged in the arena and successfully applied the foundations of Riemannian geometry to formulate his general theory of relativity. Now the concepts of hyperbolic geometry are widely used in Einstein’s special theory of relativity. One of the major and burning problem in theoretical; physics is the unification of general relativity and quantum mechanics. To achieve this goal, the author proposes for the creation of third non – Euclidean geometry.