Uma introdução a geometria não euclidiana no ensino médio: a geometria dos fractais

Abstract

The teaching of Geometry in Basic Education is based on the notions of Euclidean Geometry. Official documents such as the National Curricular Parameters and the Curricular Guidelines of the State of Bahia do not carry in their body contents that pervade Euclidean geometry. In this sense, this work has the objective, through the application of a didactic sequence in the classroom, to propose a methodological tool for the introduction of Non - Euclidean Geometry in Basic Education in the state of Bahia, focusing on the geometry of fractions. Thus, after comparing official educational documents that do not address Non-Euclidean Geometries and documents that suggest this study, this work does: a foundation on such geometries; Conceptualizes and highlights the main properties of the Fractais, focusing on the study of the fractal dimension; Applies a didactic sequence on the subject in the classroom with the aid of two software and, finally, analyzes the results obtained in the application and finishes the work conceiving that it is possible, at the level of High School, to introduce Non-Euclidean Geometry via The geometry of fractions.