Geometria Projetiva no ensino do espaço tridimensional e na estrutura de jogo de Dobble

Abstract

Projective Geometry gives us the means to demonstrate and discover properties of figures, it is a possibility to understand mathematically the study of the descriptive properties of geometric figures. And after Poncelet offering his own means to demonstrate and discover properties of figures having thus the end of the intuitive “age” of Projective Geometry. We study in this work the basic fundamentals of the projective geometry, its representation and manipulation. We used a didactic sequence based on didactic engineering, first investigating and finally a posteriori analysis. Activities will be presented where students will learn some techniques for better spatial representation using Geogebra. In the end a game is presented, called Dobble’s game, in which we made an exposition of mathematical concepts that involve the structure of the game.