A geometria projetiva como proposta de intervenção: um olhar a partir dos Teoremas de Menelau e Ceva

Abstract

This work is part of a research about Projective Geometry as pedagogic tool in High School. The research itself is part of studies developed during the Professional Master Degree in Mathematics and Education at Federal University of Juiz de Fora. We try to give a theoretical and operational approach to basic themes of Projective Geometry from the theorems of Menelau and Ceva, which assumptions are rooted in the concepts of collinearity and concurrency. It is suggested, then, a mature reflection of what we perceive in the teaching of Geometry in Brazil, mainly about the study of triangles and its relations. A historical survey of the theorems mentioned above is made and we propose some activities to take the student (subject) to face new possibilities to solve problems. It is presented the start of a proposal of methodological approach to data of a projective field research.