Bases numéricas não usuais: um breve estudo

Abstract

This work has the main objective to present the numbering systems in non-conventional bases, addressing the arithmetic operations and some properties. We will study the criteria of divisibility and parity of numbers on a different basis from the one we use today, decimal basis. Thus, during this work a reflection is made on how the study in unconventional bases can contribute to the teaching of mathematics. Chapter 1 presents a brief historical summary of the numbering systems most used by the ancient peoples of which there are still vestiges. In chapter 2 the concept of numerical basis is formally exposed and the theorem is shown that allows to represent a number on a natural basis other than one. In this chapter we still state and demonstrate some criteria of divisibility on an unusual basis. After this, some divisibility criteria are constructed in the duodecimal numbering system. Finally, chapter 3 presents a proposal for the continuing education of teachers of basic education, problems and activities that can be carried out in a training course and/or workshops, for example.