A number system with base $-\frac32$

TL;DR

This paper investigates a novel number system based on base -3/2, revealing unique properties, connections to 2-adic numbers, and fractal tilings of non-Euclidean spaces.

Contribution

It introduces and analyzes a new negative fractional base number system with distinctive mathematical properties and geometric interpretations.

Findings

Related to 2-adic number fields

Generates fractal tilings of non-Euclidean space

Exhibits properties similar yet distinct from decimal system

Abstract

In the present paper we explore a way to represent numbers with respect to the base $-\frac32$ using the set of digits $\{0,1,2\}$. Although this number system shares several properties with the classical decimal system, it shows remarkable differences and reveals interesting new features. For instance, it is related to the field of $2$-adic numbers, and to some ``fractal'' set that gives rise to a tiling of a non-Euclidean space.