Do mito da Geometria Euclidiana ao ensino das Geometrias Não Euclidianas

Non-Euclidean Geometry originated from unsuccessful attempts to prove that Euclid’s fifth postulate was a theorem. From the first four Euclidean postulates and the negation of the fifth derived other geometries whose postulates are possible in planes models, and as consistent as that in Euclidean Geometry. This article presents the Elliptical and Hyperbolic Geometry models with their postulates and concepts. A discussion of the teaching and learning of these geometries is also presented.