Noções de geometria projetiva

• Ano de defesa: 2017
• Autor(a) principal: Portela, Antonio Edilson Cardoso
• Orientador(a): Melo, Marcelo Ferreira de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Geometria projetiva; Geometria euclidiana; Geometria elíptica; Axiomas de Hilbert; Espaço tridimensional; Projective geometry; Euclidean geometry; Elliptic geometry; Hilbert's axioms; Three-dimensional space
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/25586

In this work, initially, some results of Linear Algebra are presented, in particular the study of the Vector Space R^n, which becomes, together with Analytical Geometry, the language used in the chapters that follow. We present a study from an axiomatic point of view, from the perspectives of Hilbert's axioms and we elaborate models of planes for the Euclidean, Elliptic and Projective Geometries. The validity of the Incidence and Order axioms for Euclidean Geometry is verified. In R^3, an approach is made to the study of the plane and the unitary sphere, highlighting the elliptical line obtained by the intersection of these sets, thus making an approach to the Elliptic Geometry. With the concepts and definitions studied in the Vector Space R^n, Three-dimensional Space and in the Euclidean and Elliptic Geometries we will approach the study of Projective Geometry, demonstrating propositions and verifying its axioms.