On the Inverses of Lines under the Inversion in a Generalized Taxicab Circle

Abstract

In this study, the images of lines under the inversion in a generalized taxicab circle are examined. It is observed that the image of the line not passing through the inversion center is not a generalized taxicab circle, but the closed curve. The images of the lines under the inversion mapping are investigated depending on their positions and some features related to the images are presented. Furthermore, it is concluded that the inversion in a generalized taxicab circle maps the pencil of parallel lines (except the line passing through the center) to the set of the curves passing through the inversion center.

Keywords

• Generalized taxicab distance
• Inversion in the generalized taxicab circle
• Image of the line under inversion

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