Open AccessDetour Extra Straight Lines in the Euclidean Plane
Author(s) -
I. Szalay,
B. Szalay
Publication year - 2020
Publication title -
earthline journal of mathematical sciences
Language(s) - English
Resource type - Journals
ISSN - 2581-8147
DOI - 10.34198/ejms.5221.237249
Subject(s) - euclidean geometry , line (geometry) , plane (geometry) , euclidean distance , parallel , axiom , mathematics , geometry , non euclidean geometry , combinatorics
Using the theory of exploded numbers by the axiom-systems of real numbers and Euclidean geometry, we explode the Euclidean plane. Exploding the Euclidean straight lines we get super straight lines. The extra straight line is the window phenomenon of super straight line. In general, the extra straight lines are curves in Euclidean sense, but they have more similar properties to Euclidean straight lines. On the other hand, with respect of parallelism we find a surprising property: there are detour straight lines.