Araştırma Makalesi

On Some Properties of Distance in TO-Space

Cilt: 4 Sayı: 2 30 Aralık 2020
Aksaray University Journal of Science and Engineering Kapak
Aksaray University Journal of Science and Engineering
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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

Kaynakça

  1. [1] Cromwell, P. R., Polyhedra, Cambridge University Press, 443p., 1997.
  2. [2] Thompson, A.C., Minkowski Geometry. Cambridge University Press, 346p., 1996.
  3. [3] Can, Z., Gelişgen, Ö., Kaya, R., On the Metrics Induced by Icosidodecahedron and Rhombic Triacontahedron, Scientific and Professional Journal of the Croatian Society for Geometry and Graphics (KoG), 19, 17-23, (2015).
  4. [4] Gelişgen, Ö., Can, Z., On The Family of Metrics for Some Platonic and Archimedean Polyhedra, Konuralp Journal of Mathematics, 4, 25-33, (2016).
  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).
  6. [6] Erçınar G.Z., Investigation of The Metric of Which Unit Ball is a Rhombic Dodecahedron, Eskişehir Osmangazi University. Graduate School Of Natural And Applied Sciences, Master Of Science Dissertation, 69s, Eskişehir, 2015.
  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).
  8. [8] Gelişgen Ö., Çolak Z., A Family of Metrics for Some Polyhedra, Automation Computers Applied Mathematics Scientific Journal, 24(1), 3-15, (2015).

Ayrıntılar

Birincil Dil

İngilizce

Konular

-

Bölüm

Araştırma Makalesi

Yazarlar

Yayımlanma Tarihi

30 Aralık 2020

Gönderilme Tarihi

12 Şubat 2020

Kabul Tarihi

24 Aralık 2020

Yayımlandığı Sayı

Yıl 2020 Cilt: 4 Sayı: 2

DOI

https://doi.org/10.29002/asujse.688279

IZ

https://izlik.org/JA27HB35FP

Kaynak Göster

RIS / Bibtex
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