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A New Approach for the Circular Inversion in l1- Normed Spaces
Version 1
: Received: 22 May 2024 / Approved: 22 May 2024 / Online: 22 May 2024 (15:12:02 CEST)
A peer-reviewed article of this Preprint also exists.
Ermiş, T.; Şen, A.O.; Gielis, J. A New Approach to Circular Inversion in l1-Normed Spaces. Symmetry 2024, 16, 874. Ermiş, T.; Şen, A.O.; Gielis, J. A New Approach to Circular Inversion in l1-Normed Spaces. Symmetry 2024, 16, 874.
Abstract
While there are well-known synthetic methods in the literature to find 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 giving a synthetic construction for 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; l1-Norm; Manhattan Metric, Taxicab Metric
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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