Yıl 2020, Cilt 4, Sayı 2, 113 - 126, 30.12.2020
Öz
Kaynakça
- [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).
On Some Properties of Distance in TO-Space
Yıl 2020, Cilt 4, Sayı 2, 113 - 126, 30.12.2020Öz
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.
Anahtar Kelimeler
Metric, Convex polyhedra, Truncated octahedron, Distance of a point to a line, Distance of a point to a plane, Distance between two lines
Kaynakça
- [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).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Temel Bilimler |
| Bölüm | Research Article |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Aralık 2020 |
| Başvuru Tarihi | 12 Şubat 2020 |
| Kabul Tarihi | 24 Aralık 2020 |
| Yayınlandığı Sayı | Yıl 2020, Cilt 4, Sayı 2 |
Kaynak Göster
| Bibtex | @araştırma makalesi { asujse688279, journal = {Aksaray University Journal of Science and Engineering}, issn = {}, eissn = {2587-1277}, address = {Aksaray Üniversitesi, Fen Bilimleri Enstitüsü, Merkez Kampüs, 68100 Aksaray}, publisher = {Aksaray Üniversitesi}, year = {2020}, volume = {4}, pages = {113 - 126}, doi = {10.29002/asujse.688279}, title = {On Some Properties of Distance in TO-Space}, key = {cite}, author = {Can, Zeynep} } |
| APA | Can, Z. (2020). On Some Properties of Distance in TO-Space . Aksaray University Journal of Science and Engineering , 4 (2) , 113-126 . DOI: 10.29002/asujse.688279 |
| MLA | Can, Z. "On Some Properties of Distance in TO-Space" . Aksaray University Journal of Science and Engineering 4 (2020 ): 113-126 <http://asujse.aksaray.edu.tr/tr/pub/issue/58393/688279> |
| Chicago | Can, Z. "On Some Properties of Distance in TO-Space". Aksaray University Journal of Science and Engineering 4 (2020 ): 113-126 |
| RIS | TY - JOUR T1 - On Some Properties of Distance in TO-Space AU - Zeynep Can Y1 - 2020 PY - 2020 N1 - doi: 10.29002/asujse.688279 DO - 10.29002/asujse.688279 T2 - Aksaray University Journal of Science and Engineering JF - Journal JO - JOR SP - 113 EP - 126 VL - 4 IS - 2 SN - -2587-1277 M3 - doi: 10.29002/asujse.688279 UR - https://doi.org/10.29002/asujse.688279 Y2 - 2020 ER - |
| EndNote | %0 Aksaray University Journal of Science and Engineering On Some Properties of Distance in TO-Space %A Zeynep Can %T On Some Properties of Distance in TO-Space %D 2020 %J Aksaray University Journal of Science and Engineering %P -2587-1277 %V 4 %N 2 %R doi: 10.29002/asujse.688279 %U 10.29002/asujse.688279 |
| ISNAD | Can, Zeynep . "On Some Properties of Distance in TO-Space". Aksaray University Journal of Science and Engineering 4 / 2 (Aralık 2020): 113-126 . https://doi.org/10.29002/asujse.688279 |
| AMA | Can Z. On Some Properties of Distance in TO-Space. Aksaray J. Sci. Eng.. 2020; 4(2): 113-126. |
| Vancouver | Can Z. On Some Properties of Distance in TO-Space. Aksaray University Journal of Science and Engineering. 2020; 4(2): 113-126. |
| IEEE | Z. Can , "On Some Properties of Distance in TO-Space", Aksaray University Journal of Science and Engineering, c. 4, sayı. 2, ss. 113-126, Ara. 2020, doi: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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