From the myth of Euclidean Geometry to the teaching of Non-Euclidean Geometry

Abstract

Non-Euclidean Geometry originated from unsuccessful attemptsto prove that Euclid’s fifth postulate was a theorem. From the firstfour 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.