Didàctica de superfícies planes en taxigeometria

Abstract

[en] In this work, we study some 2D surfaces in a non-Euclidean geometry: taxicab geometry, whose metric is defined by the norm l1 . To be more specifically, we discuss how some of the definitions used in Euclidean geometry apply when converted into taxicab geometry. In this way, we consider triangles with its centroid, circumcenter and incenter and its area. We also discuss the circumference, the ellipse, the hyperbola and the parabola and we introduce some results related to regular polygons. Finally, all this knowledge is used to design a didactic plan in order to bring it closer to high school students, with the aim to let them discover some mathematics different from what is usually taught at class and to work on their investigation skills and mathematimal thinking by learning about this geometry.