On Taxicab Circle Inverses of Lines

Yıl 2024, Cilt: 6 Sayı: 1, 1 - 8

Seyit Ali Aydın Ayşe Bayar

https://doi.org/10.54286/ikjm.1373938

Öz

This study conducts a thorough analytical examination of line inverses with respect to taxicab circle inversion within the analytical plane. It presents the distinctive properties exhibited by taxicab circle inverses of lines, highlighting their difference from Euclidean circle inverses.

Anahtar Kelimeler

taxicab circle inversion, taxicab inverses of lines, taxicab plane

Kaynakça

• Akça, Z., Kaya R. (1997) On the taxicab trigonometry. Journal of Inst. Math. Comput. Sci. Math. Ser.,10(3):151–159.
• Akça, Z., Kaya R. (2004) On the distance formulae in three dimensional taxicab space. Hadronic J., 27(5):521–532.
• Akça, Z., Bayar, A., Ekmekçi, S. (2007) The norm in CC-plane geometry. Pi Mu Epsilon J. 12(6): 321-324.
• Aydın, S. A. (2023) On Circular Inversions and Fractals. MSc thesis, Eskişehir Osmangazi University Institute of Science and Technology, Eskişehir, Turkey.
• Bayar A., Ekmekçi S. (2014) On circular inversions in taxicab plane. Journal of Advanced Research in Pure Mathematics, 6(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.
• Cırık, Y., Ekmekçi, S. (2022) On The Maximum Spherical Inversions. Erzincan University, Jounal of Science and Technology, 15(1):360-371.
• Childress, N. (1965) Inversion with Respect to the Central Conics. Mathematics Magazine, 38(3):147-149.
• Ekici, C., Kocayusufoğlu, İ., Akça, Z. (1998) The Norm in Taxicab Geometry. Turkish Journal of Mathematics, 22(3):295-308.
• Ekmekçi, S. (2023) A Note on the Maximum Circle Inverses of Lines in the Maximum Plane. Ikonion Journal of Mathematics, 5(2):1-9.
• Ekmekçi, S, Bilgin, Y. (2023). On the Inverses of Lines under the Inversion in a Generalized Taxicab Circle. Hagia Sophia Journal of Geometry, 5(2):41-49.
• Ekmekçi, S, Bilgin, Y. (2023). On The Inversion in the Generalized Taxicab Circle. Hagia Sophia Journal of Geometry, 5(2):50-58.
• Ekmekçi S. (2023) On The Maxımum Cırcular Inverses Of Maxımum Cırcles. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, 24(4):324-335.
• Gelişgen Ö., Ermiş T. (2019) Some Properties of Inversions in Alpha Plane, Forum Geometricorum, 19:1-9.
• Gelişgen, Ö., Ermiş, T. (2023) Inversions and Fractal Patterns in Alpha Plane. International Electronic Journal of Geometry, 16 (1):398-411.
• Kaya R., Akça Z., Özcan M., Günaltılı, İ. (2000) General equation for taxicab conics and their classification. Mitt. Math. Ges. Hamburg, 19(0):135–148.
• Krause, E. F. (1975) Taxicab Geometry. Addison –Wesley Publishing Company, Menlo Park, CA.
• Pekzorlu, A., Bayar, A. (2020) (a) On The Chinese Checkers Spherical Invesions in Three Dimensional Chinese Checker Space. Com. Fac. of Sci. Univ. of Ank. Ser. A1 M ath. and Stat., 69(2): 1498-1507.
• Pekzorlu, A., Bayar, A. (2020) (b) Taxicab Spherical Inversions in Taxicab Space. Journal of Mahani Math. Research Center, 9(1-2): 45-54.
• Pekzorlu, A., Bayar, A. (2022) On the Chinese Checkers Circular Inversions in the Chinese Checkers Plane. Hagia Sophia Journal of Geometry, 4(2):28–34.
• Ramirez, J.L., Rubiano G.N., Jurcic-Zlobec B. (2015) A Generating fractal patterns by using p-circle inversion. Fractals, 23(4):1-13.
• Schattschneider, D. J. (1984) The Taxicab Group. American Mathematical Monthly, (91):423- 428.
• Yüca, G., Can, Z. (2020) On The Circular Inversion in Maximum Plane. Ikonion Journal of Mathematics, 2(2):26-34.