Fundamentos da geometria euclidiana para o ensino dos números reais

Abstract

This paper aims to show a teaching methodology of real numbers on the grounds of Euclidean geometry. The ruler and compass are instruments of great importance in the construction of numerical sets. Based on the geometric images of the natural numbers and operations between its elements, we will gradually building the set of integers and rational numbers. We prove the existence of numbers that are not rational and a propertie of those numbers that textbooks mostly do not address: the question of density of the sets of rational and irrational in the set of real numbers. Euclidean geometry as real numbers in support facilitates student understanding and produces dynamic operations between these numbers. We also present a possible continuation of the proposed work.