THE ISOMETRY GROUP OF CHINESE CHECKER SPACE

Year 2015, Volume: 8 Issue: 2, 82 - 96, 30.10.2015

Özcan Gelişgen , Rüstem Kaya

https://doi.org/10.36890/iejg.592291

Cited By: 2

Abstract

Keywords

Group, isometry, metric, Chinese Checkers metric, Chinese Checkers geometry

References

• [1] Chen, B.-Y. and Garay, O. J., An extremal class of conformally flat submanifolds in Euclidean spaces, Acta Math. Hungar., 111(2006), no. 4, 263-303.
• [2] Duggal, Krishan L. and Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
• [3] Amstrong, M. A., Groups and Symmetry Springer-Verlag New York Inc., 1988.
• [4] Chen, G., Lines and Circles in Taxicab Geometry Master Thesis, Department of Mathematics and Computer Science, Central Missouri State Uni, 1992.
• [5] Çolakoğlu, H. B. and Kaya, R., On The Regular Polygons in The Chinese Checker Plane, Appl. Sci. 10 (2008) 29-37.
• [6] Gelişgen, Ö ., Kaya, R. and Özcan, M., Distance Formulae in the Chinese Checker Space, Int. J. Pure Appl. Math. 26 (2006), no. 1, 35–44.
• [7] Geli¸sgen, Ö . and Kaya, R., Alpha(i) Distance in n-dimensional Space, Appl. Sci. 10 (2008), 88–93.
• [8] Gelişgen, Ö. and Kaya, R., The Taxicab Space Group, Acta Math. Hungar. 122 (2009), no. 1-2, 187–200.
• [9] Kaya, R., Gelişgen, Ö ., Ekmekc¸i S. and Bayar, A., Group of Isometries of CC-Plane, Missouri J. Math. Sci. 18 (2006) 221–233.
• [10] Kaya, R., Geli¸sgen, Ö ., Ekmekçi S. and Bayar, A., On The Group of Isometries of The Plane with Generalized Absolute Value Metric, Rocky Mountain J. Math. 39 (2009), no. 2, 591–603.
• [11] Krause, E. F., Taxicab Geometry Addison - Wesley Publishing Company, Menlo Park, CA, 1975.
• [12] Martin, G. E., Transformation Geometry Springer-Verlag New York Inc., 1997.
• [13] Schattschneider, D. J., The Taxicab Group, Amer. Math. Monthly 91 (1984) 423-428.
• [14] Shen, C. F. C., The Lambda-Geometry Steiner Minimal Tree Problem and Visualization, Phd Thesis, Department of Mathematics and Computer Science, Central Missouri State Uni, 1997.
• [15] So, S. S., Recent Development in Metric Geometry, Proceedings of the 5.th National Geometry Symposioum, University of Sakarya, (Sakarya), 2005.
• [16] Thompson, A. C., Minkowski Geometry Cambridge University Press, 1996.
• [17] http://en.wikipedia.org/wiki/Rotation matrix