Numericamente igual a π

• Ano de defesa: 2013
• Autor(a) principal: Marques, Túlio Guimarães
• Orientador(a): Tonon, Durval José
• Banca de defesa: Tonon, Durval José, Couto, Maria Socorro Duarte da Silva, Baumann, Luis Rodrigo Fernandes
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Goiás
• Programa de Pós-Graduação: Programa de Pós-graduação em PROFMAT (RG)
• Departamento: Instituto de Matemática e Estatística - IME (RG)
• País: Brasil
• Palavras-chave em Português: Número π; Racionalidade ou irracionalidade do número π; Quadratura do círculo; Histórico do número
• Palavras-chave em Inglês: The number π; History of the number; The quadrature of the circle; The rationality or the irrationality of the number π
• Área do conhecimento CNPq: MATEMATICA APLICADA::ANALISE NUMERICA
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/3675

This paper aims at introducing the science which is behind the most intriguing number known to history, the number . It has challenged generations of researchers who have tried to determine its value and articulate several areas of Mathematics such as Geometry, Algebra and Analysis. The quotient of ratio between the measure of the length of a circumference and the measure of its diameter are what de ne . Some historical references such as Archimedes, Euler, Leibniz and Lindemann have signi cantly contributed with the methods to precise . The rst real academic approach to this ratio was studied by the greatest mathematician of antiquity, Archimedes, when he created an instructive process for the study of the limits. With the unsolvable problem of the quadrature of the circle, ingenious geometrical constructions are born, in order to allow the drawing, with a ruler and compass, of a square having the same area as a previous given circle. The evolution of the forms employed in order to calculate have become more evident with the introduction of Analysis applied under the foundations of Calculus. At that time, the Series come to life, indispensable tools allowing the study of the behaviour of its decimal places. Along with the advances brought by them, the investigations turned towards the classi cation concerning the rationality or the irrationality of the number. In the end, we will present some contextualization and propose exercises with the aim of stimulating the search for knowledge.