On The Inversion in the Generalized Taxicab Circle

Abstract

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.

Keywords

• Generalized taxicab distance
• Inversion in the generalized taxicab circle
• Cross-ratio
• Harmonic Conjugate

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