Uma abordagem de problemas da geometria plana do ponto de vista da geometria analítica

• Ano de defesa: 2018
• Autor(a) principal: LEITE, Wenceslau José de Souza
• Orientador(a): SILVA, Jairo Santos da
• Banca de defesa: SILVA, Jairo Santos da , SILVA, Antonio José da , VERONESE, Daniel Oliveira
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Maranhão
• Programa de Pós-Graduação: PROGRAMA DE PÓS-GRADUAÇÃO EM REDE - MATEMÁTICA EM REDE NACIONAL/CCET
• Departamento: DEPARTAMENTO DE MATEMÁTICA/CCET
• País: Brasil
• Palavras-chave em Português: Geometria plana; Geometria analítica; Problemas
• Palavras-chave em Inglês: Plane geometry; Analytical geometry; Problems
• Área do conhecimento CNPq: Geometria e Topologia
• Link de acesso: https://tedebc.ufma.br/jspui/handle/tede/2550

In general, in mathematics olympiads, the subjects collected are organized into four major groups: algebra, combinatorics, number theory, and flat geometry. This last group, in particular, is an inexhaustible source of interesting problems. Solving an Olympic problem of geometry is a task that requires a solid knowledge of the propositions and theorems related to it. In some cases, appropriate geometric constructions must be considered in order to optimize the search for a solution. Sometimes trigonometric resources can be employed for the same purpose. Still, even considering all the geometric apparatus available to the student, many problems seem to be insoluble, whereas the use of a certain technique is not always evident. In our work, we will study geometric problems extracted from mathematical olympiads around the world and analyze them through two different approaches. In the first place, we will exhibit purely Euclidean solutions, so to speak. On the other hand, we will present algebraic solutions, that is, on the basis of Cartesian geometry. In some cases, we will use the methods of Differential and Integral Calculus, given its close relationship with Descartes geometry.