Research Article
BibTex RIS Cite

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

Adnan Pekzorlu Ayşe Bayar

https://doi.org/10.31801/cfsuasmas.567533
Cited By: 3

Abstract

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.

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: 3

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.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Adnan Pekzorlu 0000-0001-9724-4084

Ayşe Bayar 0000-0001-9724-4084

Publication Date December 31, 2020
Submission Date May 19, 2019
Acceptance Date October 26, 2020
Published in Issue Year 2020 Volume: 69 Issue: 2

Cite

APA Pekzorlu, A., & Bayar, A. (2020). On the Chinese Checkers spherical inversions in three dimensional Chinese Checkers space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1498-1507. https://doi.org/10.31801/cfsuasmas.567533
AMA Pekzorlu A, Bayar A. On the Chinese Checkers spherical inversions in three dimensional Chinese Checkers space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2020;69(2):1498-1507. doi:10.31801/cfsuasmas.567533
Chicago Pekzorlu, Adnan, and Ayşe Bayar. “On the Chinese Checkers Spherical Inversions in Three Dimensional Chinese Checkers Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 2 (December 2020): 1498-1507. https://doi.org/10.31801/cfsuasmas.567533.
EndNote Pekzorlu A, Bayar A (December 1, 2020) On the Chinese Checkers spherical inversions in three dimensional Chinese Checkers space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1498–1507.
IEEE A. Pekzorlu and A. Bayar, “On the Chinese Checkers spherical inversions in three dimensional Chinese Checkers space”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1498–1507, 2020, doi: 10.31801/cfsuasmas.567533.
ISNAD Pekzorlu, Adnan - Bayar, Ayşe. “On the Chinese Checkers Spherical Inversions in Three Dimensional Chinese Checkers Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 2020), 1498-1507. https://doi.org/10.31801/cfsuasmas.567533.
JAMA Pekzorlu A, Bayar A. On the Chinese Checkers spherical inversions in three dimensional Chinese Checkers space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1498–1507.
MLA Pekzorlu, Adnan and Ayşe Bayar. “On the Chinese Checkers Spherical Inversions in Three Dimensional Chinese Checkers Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, 2020, pp. 1498-07, doi:10.31801/cfsuasmas.567533.
Vancouver Pekzorlu A, Bayar A. On the Chinese Checkers spherical inversions in three dimensional Chinese Checkers space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1498-507.

Cited By

ON THE MAXIMUM CIRCULAR INVERSES OF MAXIMUM CIRCLES
Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering
https://doi.org/10.18038/estubtda.1370728
A Note on the Maximum Circle Inverses of Lines in the Maximum Plane
Ikonion Journal of Mathematics
https://doi.org/10.54286/ikjm.1319223
Maksimum Küresel İnversiyonlar Üzerine
Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi
https://doi.org/10.18185/erzifbed.990283

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.