Research Article

On Some Properties of Distance in TO-Space

Volume: 4 Number: 2 December 30, 2020
EN

On Some Properties of Distance in TO-Space

Abstract

The aim of this work is to investigate some properties of the truncated octahedron metric introduced in the space in further studies on metric geometry. With this metric, the 3-dimensional analytical space is a Minkowski geometry which is a non-Euclidean geometry in a finite number of dimensions. In a Minkowski geometry, the unit ball is a certain symmetric closed convex set instead of the usual sphere in Euclidean space. The unit ball of the truncated octahedron geometry is a truncated octahedron which is an Archimedean solid. In this study, first, metric properties of truncated octahedron distance, d_TO, in R^2 has been examined by metric approach. Then, by using synthetic approach some distance formulae in R_TO^3, 3-dimensional analytical space furnished with the truncated octahedron metric has been found.

Keywords

References

  1. [1] Cromwell, P. R., Polyhedra, Cambridge University Press, 443p., 1997.
  2. [2] Thompson, A.C., Minkowski Geometry. Cambridge University Press, 346p., 1996.
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  5. [5] Can, Z., Çolak, Z., Gelişgen, Ö., A Note On The Metrics Induced By Triakis Icosahedron And Disdyakis Triacontahedron, Eurasian Academy of Sciences Eurasian Life Sciences Journal, 1, 1-11, (2015).
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  7. [7] Çolak Z., Gelişgen Ö., New Metrics For Deltoidal Hexacontahedron and Pentakis Dodecahedron, Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 19(3), 353-360, (2015).
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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Publication Date

December 30, 2020

Submission Date

February 12, 2020

Acceptance Date

December 24, 2020

Published in Issue

Year 2020 Volume: 4 Number: 2

APA
Can, Z. (2020). On Some Properties of Distance in TO-Space. Aksaray University Journal of Science and Engineering, 4(2), 113-126. https://doi.org/10.29002/asujse.688279

Aksaray J. Sci. Eng. | e-ISSN: 2587-1277 | Period: Biannually | Founded: 2017 | Publisher: Aksaray University | https://asujse.aksaray.edu.tr




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