A Quasi-Unary Representation of Discrete Taxicab Geometry

TL;DR

This paper introduces a quasi-unary numeral system to represent n-dimensional discrete Taxicab geometry, enabling algebraic transformations like translation and rotation of geometric shapes.

Contribution

It proposes a novel quasi-unary (QU) numeral system for representing and transforming discrete Taxicab geometry in multiple dimensions.

Findings

QU system generalizes geometric transformations

Enables algebraic manipulation of shapes in Taxicab geometry

Provides a new framework for discrete geometric representation

Abstract

In this paper we represent $n-$dimensional discrete Taxicab geometry by base--($4n+1$) numeral system. The algebraic structure of this base--($4n+1$) system is similar to unary system, we call it quasi-unary (QU) representation. QU representation generalizes translation and rotation to transform any geometrical object (shape) into another shape.