Group of All Taxicab Isometries: A Combinatorial Approach

Oki Neswan; Harry Sumartono

doi:10.37905/jjom.v6i1.23789

Group of All Taxicab Isometries: A Combinatorial Approach

Oki Neswan, Harry Sumartono

Abstract

In this work, we give a more thorough and exhaustive proof of the set of all isometries in taxicab geometry using a combinatorial approach. We show that isometries preserving taxicab distance while leaving the origin fixed are uniquely determined by how they permute the vertices of circles. Then, we use this principle to identify all isometries in taxicab geometry.

Keywords

Distance; Taxicab Distance; Isometries; Minkowski Distance

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DOI: https://doi.org/10.37905/jjom.v6i1.23789