Open AccessIntroduction into Extra Geometry of the Three-Dimensional Space II
Author(s) -
I. Szalay,
B. Szalay
Publication year - 2020
Publication title -
european journal of engineering and technology research
Language(s) - English
Resource type - Journals
ISSN - 2736-576X
DOI - 10.24018/ejeng.2020.5.8.2016
Subject(s) - euclidean geometry , geometry , non euclidean geometry , mathematics , euclidean space , plane (geometry) , space (punctuation) , absolute geometry , three dimensional space , axiom , foundations of geometry , pure mathematics , computer science , differential geometry , projective geometry , regular polygon , convex set , convex optimization , operating system
Using the theory of exploded numbers by the axiom-systems of real numbers and Euclidean geometry, we introduce concept of extra - plane of the three-dimensional space. The extra - planes are visible subsets of super-planes which are exploded Euclidean planes. We investigate the main properties of extra-planes. We prove more similar properties of Euclidean planes and extra-planes, but with respect the parllelism there is an essential difference among them.