Fine Structure Constant as a Mirror of Sphere Geometry

A path is de ned as the vector’s sum of the translation and rotation component of the length unit belonging to the mass entity in motion on the sphere. The ne structure constant is an irrational number being a mirror of the path complexity as well as the sphere curvature where the path is made. The inverse value in the Euclidean plane yields α 1=√π^2 + 137^2. The inverse ne structure constant on the elliptic sphere is smaller and on the hyperbolic sphere is greater. The electron in the Hydrogen atom should move on the elliptic sphere of the radius of 3679 Compton wavelengths of the electron according to the CODATA 2012 recommended empirical value α 1 = 137.035999074. Such a small sphere radius implies the heterogeneous curvature of the present universe.