UM ESTUDO DO MODELO DO SEMIPLANO DE POINCARÉ

Abstract

This work presents an introductory study on the model of the Poincaré Semiplane, one of the models that give meaning to Hyperbolic Geometry. The proposal was to study the model of the Poincaré Semiplane knowing first the historical context of the emergence of Geometry Non-Euclidean, in which several mathematicians contributed notions that were valid for this new Geometry, which emerged after the difficulty presented in understanding the Fifth Euclid's postulate. Before studying about the chosen model, it will be explained what would be a model using Analytical Geometry. Then, the model will be analyzed of the Poincaré Semiplane, making a study of points and lines, relative positions between h-lines, distance between points and angles between h-lines. Finally, it presents a study on of hyperbolic triangles, from theorems, lemma and corollary. The objective of the work was achieved from bibliographic research.