Two Findings for the Origin of Third Non Euclidean Geometry

Abstract

It is well known that the classical Euclidean geometry is one of the foundations for Newtonian mechanics and modern engineering and physical fields. The formulae of hyperbolic geometry are widely applied the study the properties of atomic particles. Also, this geometry has nice applications to Einstein’s special relativity theory. General relativity (GR) is the geometrical description of gravitation. The GR relies on Riemannian non Euclidean concepts. The famous French mathematician used to tell time and again that as long as algebra and geometry have been separated, their progress have been slow and their uses limited, but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection. Also, Einstein dreamed of to formulate the laws of physics in algebraic equations like E = mc2. Keeping this mind, the author extended algebraic operations to non Euclidean geometries and found two surprising results (http://www.learner.org/courses/mathilluminated/units/8/textbook/04.php, http://www.sjsu.edu/faculty/watkins/sphere.htm, http://www.math.washington.edu/~king/coursedir/m445w04/notes/ref/refs-sphere.html, http://www.britannica.com/EBchecked/topic/559649/spherical-geometry, http://en.wikipedia.org/wiki/Hyperbolic_geometry, http://www.math.ecnu.edu.cn/~lfzhou/others/cannon.pdf, http://en.wikibooks.org/wiki/Geometry/Hyperbolic_and_Elliptic_Geometry, http://www.math.cornell.edu/~mec/mircea.html).