Geometria do táxi versus geometria euclidiana: explorando as diferenças e aplicações na Educação Básica

Abstract

Euclidean geometry is based and structured by Euclid of Alexandria in the work ”The Elements”, which is a predominant mathematical and geometric treatise until today. However, some structural flaws allowed the emergence of other geometries, one of them being the taxicab geometry. As a result, this dissertation aims to present a didactic sequence that shows Basic Education students, in a contextualized way, the existing geometries, as well as making comparisons between the euclidean and taxicab geometries. The didactic sequence in question consists of three activities that make it possible to awaken students’ interest in the study of the taxicab distance until the consolidation of the concept of conics, passing through the construction and comparison of the relative formulas of the euclidean and taxicab distances. The entire theoretical foundation, from the concept of metrics, the historical context of the appearance of the taxicab geometry and a didactic pedagogical support material is available for teachers, which transcribes each of the activities with suggestions, objectives and skills to be worked on with the students.