TY - JOUR

T1 - A Number System with Base −32

AU - Rossi, Lucia

AU - Thuswaldner, Jörg

PY - 2022

Y1 - 2022

N2 - n the present article we explore a way to represent numbers with respect to the base −32 using the set of digits {0, 1, 2}. Although this number system shares several properties with the classical decimal system, it shows some remarkable differences and reveals interesting new features. For instance, it is related to the field of 2-adic numbers, and to a self-affine “fractal” set that gives rise to a tiling of a non-Euclidean space. Moreover, it has relations to Mahler’s 32-problem and to the Josephus problem.

AB - n the present article we explore a way to represent numbers with respect to the base −32 using the set of digits {0, 1, 2}. Although this number system shares several properties with the classical decimal system, it shows some remarkable differences and reveals interesting new features. For instance, it is related to the field of 2-adic numbers, and to a self-affine “fractal” set that gives rise to a tiling of a non-Euclidean space. Moreover, it has relations to Mahler’s 32-problem and to the Josephus problem.

U2 - 10.1080/00029890.2022.2061281

DO - 10.1080/00029890.2022.2061281

M3 - Article

VL - 129.2022

SP - 539

EP - 553

JO - The American mathematical monthly

JF - The American mathematical monthly

SN - 1930-0972

IS - 6

ER -