Abstract
References
- [1] Cromwell, P. R., Polyhedra, Cambridge University Press, 443p., 1997.
- [2] Thompson, A.C., Minkowski Geometry. Cambridge University Press, 346p., 1996.
- [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] Gelişgen, Ö., Can, Z., On The Family of Metrics for Some Platonic and Archimedean Polyhedra, Konuralp Journal of Mathematics, 4, 25-33, (2016).
- [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] 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] Çolak Z., Gelişgen Ö., New Metrics For Deltoidal Hexacontahedron and Pentakis Dodecahedron, Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 19(3), 353-360, (2015).
- [8] Gelişgen Ö., Çolak Z., A Family of Metrics for Some Polyhedra, Automation Computers Applied Mathematics Scientific Journal, 24(1), 3-15, (2015).
- [9] Gelişgen, Ö., Ermiş, T., Günaltılı, İ., A Note About The Metrics Induced by Truncated Dodecahedron And Truncated Icosahedron, International Journal Of Geometry, 2(6), 5 – 16, (2017).
- [10] Milmann, R. S., Parker, G. D., Geometry; A Metric Approach with Models, Springer, 361p., 1991.
- [11] Divjak, B., Notes on taxicab geometry, Scientific and Professional Information Journal of Croatian Society for Constructive Geometry and Computer Graphics (KoG), 5, 5–9, (2000).
- [12] Çolak, Z., Can, Z., Some Distance Properties Of Two Spaces Induced By Dual Convex Polyhedra, International Journal Of Geometry, 7, 12-24, (2018).
- [13] Akça, Z., Kaya, R., On The Distance Formulae in Three Dimensional Taxicab Space, Hadronic Journal, 27(5), 521-532, (2004).
- [14] Gelişgen, Ö., Kaya, R., Özcan, M. 2006, Distance Formulae in the Chinese Checker Space, International Journal of Pure and Applied Mathematical (IJPAM), 26(1), 35-44, (2006).
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
Metric Convex polyhedra Truncated octahedron Distance of a point to a line Distance of a point to a plane Distance between two lines
References
- [1] Cromwell, P. R., Polyhedra, Cambridge University Press, 443p., 1997.
- [2] Thompson, A.C., Minkowski Geometry. Cambridge University Press, 346p., 1996.
- [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] Gelişgen, Ö., Can, Z., On The Family of Metrics for Some Platonic and Archimedean Polyhedra, Konuralp Journal of Mathematics, 4, 25-33, (2016).
- [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] 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] Çolak Z., Gelişgen Ö., New Metrics For Deltoidal Hexacontahedron and Pentakis Dodecahedron, Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 19(3), 353-360, (2015).
- [8] Gelişgen Ö., Çolak Z., A Family of Metrics for Some Polyhedra, Automation Computers Applied Mathematics Scientific Journal, 24(1), 3-15, (2015).
- [9] Gelişgen, Ö., Ermiş, T., Günaltılı, İ., A Note About The Metrics Induced by Truncated Dodecahedron And Truncated Icosahedron, International Journal Of Geometry, 2(6), 5 – 16, (2017).
- [10] Milmann, R. S., Parker, G. D., Geometry; A Metric Approach with Models, Springer, 361p., 1991.
- [11] Divjak, B., Notes on taxicab geometry, Scientific and Professional Information Journal of Croatian Society for Constructive Geometry and Computer Graphics (KoG), 5, 5–9, (2000).
- [12] Çolak, Z., Can, Z., Some Distance Properties Of Two Spaces Induced By Dual Convex Polyhedra, International Journal Of Geometry, 7, 12-24, (2018).
- [13] Akça, Z., Kaya, R., On The Distance Formulae in Three Dimensional Taxicab Space, Hadronic Journal, 27(5), 521-532, (2004).
- [14] Gelişgen, Ö., Kaya, R., Özcan, M. 2006, Distance Formulae in the Chinese Checker Space, International Journal of Pure and Applied Mathematical (IJPAM), 26(1), 35-44, (2006).
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | December 30, 2020 |
| Submission Date | February 12, 2020 |
| Acceptance Date | December 24, 2020 |
| Published in Issue | Year 2020 |
Aksaray J. Sci. Eng. | e-ISSN: 2587-1277 | Period: Biannually | Founded: 2017 | Publisher: Aksaray University | https://asujse.aksaray.edu.tr
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