Maksimum Küresel İnversiyonlar Üzerine

Bu çalışmada, maksimum metrikle donatılmış uzayda maksimum küresel inversiyonlar ve özellikleri verilerek, maksimum küresel inversiyonlar altında çifte oran, harmonik eşlenik, doğru, düzlem ve kürenin maksimum küresel inversleri inceleniyor.

Anahtar Kelimeler:

: maksimum metrik, küresel inversiyon, maksimum uzay

On The Maximum Spherical Inversions

In this study, the inversions with respect to the sphere and some of its properties in the space denoted with the maximum metric are presented, the maximum spherical inverse of the cross ratio, the harmonic conjugate, the line, the plane and sphere are studied.

Keywords:

maximum metric, spherical inversion, maximum space,

PDF

___

Akça, Z. and Kaya R. 1997. “On the taxicab trigonometry”, J. of Inst. Math. Comput. Sci. Math. Ser.,, 10, 3, 151–159.
Akça, Z. and Kaya R. 2004 “On the distance formulae in three dimensional taxicab space”,Hadronic J., vol. 27, no. 5, 521–532.
Bayar A. and Kaya R. 2011. “On Isometries Of \mathbb{R}_{\pi n}^2”, Hacettepe Journal Of Mathematics And Statistics, 40, 5, 673–679.
Bayar A., Ekmekçi S. 2014, “On circular inversions in taxicab plane”, Journal of Advanced Research in Pure Mathematics, Vol. 6, Issue 4, 33-39.
Bayar A., Ekmekçi S. 2015. “On Complex Numbers and Taxicab Plane.” Mathematical Sciences & Applications E-Notes, 3, 1, 58–64.
Blair, D. E. 2000, “Inversion Theory and Conformal Mapping”, American Math. Society, 9,1.
Childress, N.1965, “Inversion with Respect to the Central Conics”, Mathematics Magazine, Vol.38(3).
Ermiş, T., Kaya, R. 2013, “On The Isometries of 3-Dimensional MaximumSpace”, Konuralp Journal of Mathematics, 3,1,103-114.
Gdawiec, K. 2014, “Star-shaped set inversion fractals”, Fractals, 22, 4, 1-7.
Gelişgen Ö., Ermiş T. 2019, “Some Properties of Inversions in Alpha Plane”, Forum Geometricorum, 19, 1-9.
Kaya R., Akça Z., Özcan M. and Günaltılı, İ. 2000,“General equation for taxicab conics and their classification,” Mitt. Math. Ges. Hamburg, vol. 19, no. 0, 135–148.
Nickel, J.A. 1995, “A Budget of Inversion”, Math. Comput. Modelling, Vol:21,6,87-93.
Pekzorlu, A. 2019, “Bazı Öklidyen Olmayan Geometrilerde İnversiyonlar Üzerine”, Doktora Tezi, Eskişehir Osmangazi Üniversitesi Fen Bilimleri Enstitüsü.
Pekzorlu, A., Bayar, A. 2020, “On The Chinese Checkers Spherical Invesions In Three Dimensional Chinese Checker Space”, Com. Fac. of Sci. Univ. of Ank. Ser. A1 Math. and Stat., 69, 2, 1498-1507.
Pekzorlu, A., Bayar, A. 2020, “Taxicab Spherical Invesions In Taxicab Space”, Journal of Mahani Math. Research Center, Vol:9, no 1-2, 45-54.
Ramirez, J.L. 2013, “An Introduction to Inversion in an Ellipse”, arXiv:1309.6378v1.
Ramirez, J.L. 2014, “Inversions in an Ellipse”, Forum Geometricorum, Vol. 14,107–115.
Ramirez, J.L., Rubiano G.N. 2014, “A Geometrical Construction of Inverse Points With Respect To An Ellipse”, International Journal Of Mathematical Education In Science And Technology, Vol. 45, Issue 8, 1254-1259.
Ramirez, J.L., Rubiano G.N. 2016, “ A Generalization of the spherical inversion”, International Journal Of Mathematical Education In Science And Technology, Vol. 48, Issue 1, 132-149.
Ramirez, J.L., Rubiano G.N., Jurcic-Zlobec B 2015, “A Generating fractal patterns by using p-circle inversion”, Fractals, 23(4), 1-13.
Salihova, S. 2006, “Maksimum Metriğinin Geometrisi Üzerine”, Doktora Tezi, Eskişehir Osmangazi Üniversitesi Fen Bilimleri Enstitüsü.
Yüca, G., Can, Z. 2020, “On The Circular Inversion in Maximum Plane”, Ikonion Journal Of Mathhematics, Vol.2, Issue 2.