The Generalized Taxicab Group
Yıl: 2018 Cilt: 11 Sayı: 2 Sayfa Aralığı: 83 - 89 Metin Dili: İngilizce İndeks Tarihi: 01-08-2019
The Generalized Taxicab Group
Öz: In this study, we determine the generalized taxicab group consisting all isometries of the real planeendowed with the generalized taxicab metric. First we develop natural analogues of Euclideanreflection and rotation notions, and then determine all isometries in the generalized taxicab plane.Finally, we show that the generalized taxicab group is semidirect product of the translation groupand the generalized taxicab symmetry group of the unit generalized taxicab circle, as Euclideangroup. We also see that there are transformations of the real plane onto itself which preserve thegeneralized taxicab distance, but not preserve the Euclidean distance.
Anahtar Kelime: Konular:
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- Akça, Z. and Kaya, R., On the taxicab trigonometry. Jour. of Inst. of Math. Comp. Sci. (Math. Ser.) 10 (1997), no.3, 151-159.
- Çolakoğlu, H.B. and Kaya, R., A generalization of some well-known distances and related isometries. Math. Commun. 16 (2011), 21-35.
- Ekmekçi, E., Bayar, A. and Altıntaş, A.K., On the group of isometries of the generalized taxicab plane. International Journal of Contemporary Mathematical Sciences 10 (2015), no.4, 159-166.
- Ekmekçi, S., Akça, Z. and Altıntaş, A.K., On trigonometric functions and norm in the generalized taxicab metric. Mathematical Sciences And Applications E-Notes 3 (2015), no.2, 27-33.
- Gelişgen, Ö. and Kaya, R., The taxicab space group. Acta Math. Hung. 122 (2009), no.1-2, 187-200.
- Kaya, R., Akça, Z., Günaltılı, İ. and Ö zcan, M., General equation for taxicab conics and their classification. Mitt. Math. Ges. Hamburg 19 (2000), 135-148.
- Kocayusufoglu, İ. and Özdamar, E., Isometries of taxicab geometry. Commum. Fac. Sci. Univ. Ank. Series A1 47 (1998), 73-83.
- Krause, E.F., Taxicab Geometry. Dover, New York, 1986.
- Martin, G.E., Transformation Geometry. Springer-Verlag, New York Inc., 1997.
- Menger, K., You Will Like Geometry. Guidebook of Illinois Institute of Technology Geometry Exhibit, Museum of Science and Industry, Chicago, Illinois, 1952.
- Richard, S. M. and George, D.P., Geometry, A Metric Approach With Models. Springer-Verlag, New York, 1981.
- Schattschneider, D.J., The taxicab group. American Mathematical Monthly 91 (1984), no.7, 423-428.
- Thompson, K.P. and Dray T., Taxicab Angles and Trigonometry. The Pi Mu Epsilon Journal 11 (2000), no.2, 87-96.
- Thompson, K.P., The nature of length, area, and volume in taxicab geometry. International Electronic Journal of Geometry 4 (2011), no.2, 193-207.
- Wallen, L.J., Kepler, the taxicab metric, and beyond: An isoperimetric primer. The College Mathematics Journal 26 (1995), no.3, 178-190.
| APA | Çolakoğlu H (2018). The Generalized Taxicab Group. , 83 - 89. |
| Chicago | Çolakoğlu Harun Barış The Generalized Taxicab Group. (2018): 83 - 89. |
| MLA | Çolakoğlu Harun Barış The Generalized Taxicab Group. , 2018, ss.83 - 89. |
| AMA | Çolakoğlu H The Generalized Taxicab Group. . 2018; 83 - 89. |
| Vancouver | Çolakoğlu H The Generalized Taxicab Group. . 2018; 83 - 89. |
| IEEE | Çolakoğlu H "The Generalized Taxicab Group." , ss.83 - 89, 2018. |
| ISNAD | Çolakoğlu, Harun Barış. "The Generalized Taxicab Group". (2018), 83-89. |
| APA | Çolakoğlu H (2018). The Generalized Taxicab Group. International Electronic Journal of Geometry, 11(2), 83 - 89. |
| Chicago | Çolakoğlu Harun Barış The Generalized Taxicab Group. International Electronic Journal of Geometry 11, no.2 (2018): 83 - 89. |
| MLA | Çolakoğlu Harun Barış The Generalized Taxicab Group. International Electronic Journal of Geometry, vol.11, no.2, 2018, ss.83 - 89. |
| AMA | Çolakoğlu H The Generalized Taxicab Group. International Electronic Journal of Geometry. 2018; 11(2): 83 - 89. |
| Vancouver | Çolakoğlu H The Generalized Taxicab Group. International Electronic Journal of Geometry. 2018; 11(2): 83 - 89. |
| IEEE | Çolakoğlu H "The Generalized Taxicab Group." International Electronic Journal of Geometry, 11, ss.83 - 89, 2018. |
| ISNAD | Çolakoğlu, Harun Barış. "The Generalized Taxicab Group". International Electronic Journal of Geometry 11/2 (2018), 83-89. |
