hsjg Hagia Sophia Journal of Geometry 2687-4261 Salim YÜCE Algebraic and Differential Geometry Cebirsel ve Diferansiyel Geometri On The Inversion in the Generalized Taxicab Circle https://orcid.org/0000-0003-2820-2096 Ekmekçi Süheyla ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ https://orcid.org/0000-0001-6867-1220 Bilgin Yeliz ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ 12 30 2023 5 2 50 58 10 12 2023 12 16 2023 Copyright © 2019, Hagia Sophia Journal of Geometry 2019 Hagia Sophia Journal of Geometry

In this study, inversions in generalized taxicab circles are defined and their properties are presented. The results obtained by examining the images of points under inversions in generalized taxicab circles are provided. Additionally, the concept of the directed generalized taxicab length of a line segment is introduced. Based on this concept, the definitions of the generalized taxicab cross-ratio and the generalized taxicab harmonic conjugate are given, along with some of their properties. The impact of inversion in the generalized taxicab circle on these concepts is investigated.

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