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Article

The Parallel Postulate is Depended on the Other Axioms

1Larnaca, Cyprus


Applied Mathematics and Physics. 2013, Vol. 1 No. 4, 129-142
DOI: 10.12691/amp-1-4-6
Copyright © 2013 Science and Education Publishing

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.

Correspondence to: Markos  Georgallides, Larnaca, Cyprus. Email: georgallides.marcos@cytanet.com.cy

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.

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