A New Approach to Circular Inversion in <i>l</i>₁-Normed Spaces

Abstract

While there are well-known synthetic methods in the literature for finding the image of a point under circular inversion in l2-normed geometry (Euclidean geometry), there is no similar synthetic method in Minkowski geometry, also known as the geometry of finite-dimensional Banach spaces. In this study, we have succeeded in creating a synthetic construction of the circular inversion in l1-normed spaces, which is one of the most fundamental examples of Minkowski geometry. Moreover, this synthetic construction has been given using the Euclidean circle, independently of the l1-norm.

Keywords

• finite-dimensional Banach spaces
• Minkowski geometry
• metric geometry
• <i>l</i>₁-norm
• Manhattan metric
• taxicab metric