The parallel postulate, the other four and Relativity

摘要

Because of Geometers scarcity, I was instigated to republish this article and to locate the weakness of prooving this Axiom. Weakness created the Non-Euclid geometries which deviated GR in Space-time confinement, so, not conceiving the beyond Planck`s existence, not explaining the WHY speed of light is constant, and thus the whole universe. In the manuscript is prooved that parallel postulate is only in Plane (three points only and not a Spherical triangle) based on the four Postulates for Constructions, where all properties of Euclidean geometry compactly exist as Extrema on points, lines, planes, circles and spheres. Projective, Hyperbolic and Elliptic geometry is proved to be an Extrema (deviations) in Euclidean geometry where on them Einstein's theory of general relativity is implicated approximately to the properties of physical space. The universally outstanding denial perception that Proof by geometric logic only is inaccessible, is now contradicted, and this current knowledge is widely extended.