Um estuo dos modelos da geometria hiperbólica

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 know...

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Detalles Bibliográficos
Autor: Magalhães, José Messias [UNESP]
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2015
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:portugués
OAI Identifier:oai:repositorio.unesp.br:11449/134147
Acceso en línea:http://hdl.handle.net/11449/134147
http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/19-01-2016/000857257.pdf
Access Level:acceso abierto
Palabra clave:Geometry, Non-Euclidean
Geometria não-euclidiana
Geometria hiperbolica
Axiomas
Descripción
Sumario: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