On the Chinese Checkers spherical inversions in three dimensional Chinese Checkers space

Year 2020, Volume: 69 Issue: 2, 1498 - 1507, 31.12.2020

Adnan Pekzorlu , Ayşe Bayar

https://doi.org/10.31801/cfsuasmas.567533

Cited By: 4

Abstract

In this paper, we study an inversion with respect to a Chinese checkers sphere in the three dimensional Chinese Checkers space, and prove several properties of this inversion. We also study cross ratio, harmonic conjugates and the inverse images of lines, planes and Chinese Checkers spheres in three dimensional Chinese Checkers space.

Keywords

Chinese Checkers space, Chinese Checkers sphere, inversion, harmonic conjugates

References

• Blair, D., Inversion Theory and Conformal Mapping, Student Mathematical Library, American Mathematical Society, 9, 2000.
• Blåsjö Jakob, V., Steiner's Systematische Entwickelung: The Culmination of Classical Geometry, The Mathematical Intelligencer, 31(1) (2009), 21-29.
• Childress, N., Inversion with respect to the central conics, Mathematics Magazine, 38(3) (1965).
• Deza, E., Deza, M., Dictionary of Distances, Elsevier Science, 2006.
• Gelisgen, Ö., Kaya, R., The Taxicab Space Group, Acta Mathematica Hungarica, 122 (1) (2008), 187-200. Kaya, R., Akça, Z., Günaltılı, İ., Özcan, M., General Equation For taxicab Conics and Their Classification, Mitt. Math. Ges. Hamburg, 19 (2000), 135-148. Krause, E. F., Taxicab Geometry, Addison-Weley, Menlo Park, California,1975.
• Menger, K., You Will Like Geometry, Guildbook of Illinois Institute of Technology Geometry Exhibit, Museum of Science & Industry,Chicago, Illinois, 1952.
• Minkowski, H., Gasammelte Abhandlungen, Chelsea Publishing Co., New York,1967. Nickel, J.A., A Budget of Inversion, Math. Comput. Modelling, 21(6) (1995), 87-93.
• Özcan, M., Kaya, R., On the Ratio of Directed Lengths in the Taxicab Plane and Related Properties, Missouri Journal of Mathematical Sciences, 14(2) (2002).
• Gelisgen, Ö., Kaya, R., Özcan, M., Distance Formulae in the Chinese Checker Space, Int.J. Pure Appl. Math., 26(1) (2006), 35-44. Ramirez, J.L., An Introduction to Inversion in an Ellipse, arXiv:1309.6378v1, Sept. 2013. Schattschneider, D. J., The Taxicab Group, American Mathematical Monthly, 91 (1984), 423-428.
• Kaya, R., Gelisgen, Ö., Bayar, A., Ekmekçi, S., Group of Isometries of CC-Plane, Missouri J. Math. Sci., 18 (2006), 221-233.
• Ramirez, J.L., Rubiano, G. N., A generalization of the spherical inversion, International Journal of Mathematical Education in Science and Technology, 48(1) (2016), 132-149. Bayar,A., Ekmekçi, S., On circular inversions in taxicab plane. J. Adv. Res. Pure Math., 6(4) (2014), 33--39.
• Akca, Z., Kaya, R., On the Distance Formulae In three Dimensional Taxicab Space, Hadronic Journal, 27 (2006), 521-532. Gelisgen, Ö., Ermiş, T., Some properties of inversions in alpha plane, Forum Geometricorum, 19 (2019), 1-9.
• Ramirez, J.L., Rubiano, G. N., Jurcic-Zlobec, B., Generating fractal patterns by using p-circle, Fractals, 23(4) (2015), 1-13. Pekzorlu, A., Bayar, A., Taxicab Spherical Inversions in Taxicab Space, Journal Of Mahani, Math. Research Center, 9(1-2) (2020), 45-54.
• Chen, G., Lines and Circles in Taxicab Geometry Master Thesis, Department of Mathematic and Computer Science, Central Missouri State Uni, 1992.