Números construtíveis.

Abstract

The aim of this work is to contribute to a pedagogical practice that enables students realize the use of geometric constructions, as well as the importance of the same to solve problems involving constructible numbers. For this, we present historical facts about geometry and geometric constructions in order to know more about the emergence of such content and, in the case of constructions, which are the only tools and procedures that can be used to perform them. We will see, therefore, that these tools are the ruler and compass and that procedures are tracing straight lines and circles. Moreover, we solved several problems involving such constructions, with the help of GeoGebra, trying to stimulate both the teaching of constructible numbers, as the use of dynamic geometry environment. Also we present three classical Greek problems, whose solution, with ruler and compass, is impossible, unless approximately. We further emphasize the definition and some properties of constructible numbers, each showing through constructions. Finally, we show examples and suggest activities that we believe will encourage the construction of some numbers and the use of GeoGebra.