Uma proposta para solução de problemas com a utilização dos axiomas da geometria projetiva

Abstract

This paper presents solutions to problems using axioms of projective geometry and one problem with solution via Desargues ´ Theorem. In addition, it contains demonstrations of Pappus Theorem, Desargues ¨ Theorem and Pascal´s Theorem. To support this work, we analyzed geometry instruction and the historical development of projective geometry, also presenting basic preliminary concepts of analytic geometry and projective geometry that guided the axioms that are used along with the free Geogebra software for solutions of the problems proposed in the work. There was great concern about the use of language that would be adequate for high school students, since the theory is somewhat advanced for elementary school. At the end of the paper there is a proposal for how to create a bridge between the concepts of projective geometry and analytic geometry and how these can be applied at a high school level.