Construções geométricas, insolubilidade de soluções dos problemas clássicos e aplicações no ensino básico

Abstract

The study of Geometry, through geometric constructions, is very important for the development of logical-deductive reasoning. This work aimed to show the importance of such geometric constructions, which are performed with non - graduated ruler and compass, analyzing the possibility of solving problems involving these instruments and knowledge about the constructible numbers. To this end, a brief history of geometry and geometric constructions will be presented with the objective of knowing more about its appearance and about how the constructions were used. We will analyze, on the construt vel points and we will see that the procedures to obtain such points come from the drawing of lines and of circumferences. In addition, we will present some elementary constructions to assist in the resolution of construction problems. Backed up in the theoretical foundation, we present the impossibility of solving with a ruler and compass of the three classical Greek problems, whose solution is not possible, except approximately. Finally, we will show examples of geometrical construction application problems with Euclidean instruments and the use of GeoGebra as suggestions for activities for basic education.