Sobre a construtibilidade dos números: propriedades, a espiral de Theodorus e atividades propostas para o ensino básico de matemática

Abstract

In this work we will address the constructible numbers and the famous spiral of Theodorus, a drawing figure in the shape of a spiral built with a ruler and compass in one plane and the result of overlapping right triangles, where the hypotenuse of an overlapping triangle, where the hypotenuse of a triangle superimposed is also one of the legs of another triangle, and one of the readings of this figure is to illustrate the fact that irrational numbers of type √ n are constructable numbers, whatever n ∈ N. We introduce the definition of the concept of constructible number, we give examples, we study the basic principles of ruler and compass constructions, we present a historical synt on these subjects, in particular, the Theodorus spiral. We take the opportunity to share L A T E Xcommand sets capable of producing figures on these subjects.