Sumartono, Harry
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Group of All Taxicab Isometries: A Combinatorial Approach Neswan, Oki; Sumartono, Harry
Jambura Journal of Mathematics Vol 6, No 1: February 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i1.23789

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.