Os quadriláteros de Saccheri e o surgimento da geometria hiperbólica

• Ano de defesa: 2018
• Autor(a) principal: Vieira, Juniano Vergna
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Espírito Santo; BR; Mestrado Profissional em Matemática em Rede Nacional; Centro de Ciências Exatas; UFES; Programa de Pós-Graduação em Matemática em Rede Nacional
• Palavras-chave em Português: Postulado; Quadrilátero; Euclides; Saccheri; Geometria; Geometria hiperbólica; Quadrilátero de Saccheri; Matemática; 51
• Link de acesso: http://repositorio.ufes.br/handle/10/7550

In this work we begin by making an approach on the historical importance of the Euclid’s Fifth Postulate, which for not being so obvious, has been the subject of several attempts at demonstration. Subsequently, we present some aspects of Neutral Geometry, so it is called because the Parallel Postulate is not assumed, which, as we shall see, is a statement equivalent to the Fifth Postulate. Of all those who strove to demonstrate the Fifth Postulate, we highlight in chapter 4 the results obtained by the jesuit priest Gerolamo Saccheri.In their results, the main figure used by is a quadrilateral ABCD, with AB = CD and right angles at A and D ( Saccheri quadrilateral). In his attempt to demonstrate Saccheri presents several interesting propositions, which contributed significantly to the emergence of Hyperbolic Geometry. In the following chapters are presented some affirmations equivalent to the Fifth Postulate, besides some axioms and theorems necessary for an introduction to the study of Hyperbolic Geometry.