Detour Extra Straight Lines in the Euclidean Plane

  • I. Szalay Mathematical Institute, University of Szeged, Hungary
  • B. Szalay Mathematical Institute, University of Szeged, Hungary
DOI: https://doi.org/10.34198/ejms.5221.237249
Keywords: exploded number, straight lines (Euclidean-, super- and extra-sense), parallelism

Abstract

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.

References

I. Szalay, Exploded and compressed numbers, Acta Mathematica Academiae Paedagogicae Nyíregyháziensis (AMAPN) 18 (2002), 33-51.

I. Szalay, Explosion and compression by numbers, International Journal of Applied Mathematics 18(1) (2005), 33-60.

sites.math.washington.edu/~hart/m524/realprop.pdf

I. Szalay, Exploded and Compressed Numbers: Enlargement of Universe, Parallel Universes, Extra Geometry, LAP LAMBERT Academic Publishing, Saarbrücken, Germany, 2016.

https://en.wikipedia.org/wiki/Euclidean_geometry (accessed: on 6th April 2020)

I. Szalay and B. Szalay, Introduction into the extra geometry of the three-dimensional space I, European Journal of Engineering Research and Science (EJERS) 5(5) (2020), 538-544. https://doi.org/10.24018/ejers.2020.5.5.1856

Published
2020-09-18
How to Cite
Szalay, I., & Szalay, B. (2020). Detour Extra Straight Lines in the Euclidean Plane . Earthline Journal of Mathematical Sciences, 5(2), 237-249. https://doi.org/10.34198/ejms.5221.237249
Issue
Vol 5 No 2 (2021)
Section
Articles


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