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## On Some Properties of Distance in TO-Space

#### Zeynep CAN [1]

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.
Metric, Convex polyhedra, Truncated octahedron, Distance of a point to a line, Distance of a point to a plane, Distance between two lines
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Primary Language en Basic Sciences Research Article Orcid: 0000-0003-2656-5555Author: Zeynep CAN (Primary Author)Institution: Aksaray UniversityCountry: Turkey Application Date : February 12, 2020 Acceptance Date : December 24, 2020 Publication Date : December 30, 2020
 Bibtex @research article { 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 University}, 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 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 (December 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, vol. 4, no. 2, pp. 113-126, Dec. 2021, doi:10.29002/asujse.688279

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