Um estuo dos modelos da geometria hiperbólica

• Ano de defesa: 2015
• Autor(a) principal: Magalhães, José Messias [UNESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Geometry, Non-Euclidean; Geometria não-euclidiana; Geometria hiperbolica; Axiomas
• Link de acesso: http://hdl.handle.net/11449/134147; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/19-01-2016/000857257.pdf

The aim of this dissertation is to introduce the main concepts and results of hyperbolic geometry including the non-existence of rectangles. This statement is one of the many di erences between Euclidean geometry and Hyperbolic geometry from the negation of the Fifth Axiom of Euclid or as it is known, the Axiom of parallel of Euclid. In the nal part of this work we shall cover three main models of Hyperbolic Geometry: Beltrami-Klein, Poincaré Disk and the Poincaré Half Plane. We also demonstrate that these models are isomorphic