The Parallel Postulate is Depended on the Other Axioms

Markos Georgallides^1,

¹Larnaca, Cyprus

Cite this paper:
Markos Georgallides. The Parallel Postulate is Depended on the Other Axioms. Applied Mathematics and Physics. 2013; 1(4):129-142. doi: 10.12691/amp-1-4-6

Abstract

In the manuscript is proved that parallel postulate is only in Plane (three points only) and is 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.

Keywords:
parallel postulate Euclid geometry

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Figures

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