A Pure Taxicab Perspective on Isometries

TL;DR

This paper explores the isometries of the plane under the taxicab metric and applies these findings to prove a classical Euclidean proposition within taxicab geometry.

Contribution

It explicitly characterizes the isometries of the taxicab plane and demonstrates their use in proving Euclidean propositions in taxicab geometry.

Findings

Taxicab isometries are explicitly characterized.

Euclid's Proposition I.5 holds under certain conditions in taxicab geometry.

The paper bridges Euclidean and taxicab geometries through isometry analysis.

Abstract

In this paper, we explicitly show the various isometries of the plane under the taxicab metric. We then use these isometries to prove that Euclid's proposition I.5 for isoscelese triangles is true under certain circumstances in taxicab geometry.