Número Irracionais e transcendentes

• Ano de defesa: 2015
• Autor(a) principal: Oliveira, Gilberto Antonio de [UNESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Matemática - Estudo e ensino; Aritmetica - Estudo e ensino; Numeros irracionais; Campos algébricos; Numeros transcendentes; Matemática - Metodologia
• Link de acesso: http://hdl.handle.net/11449/127674; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/31-08-2015/000844541.pdf

Irrational and transcendental numbers intrigued mathematicians since the beginning of mathematical development. Proving the irrationality or transcendence of a number can be a subject very complicated, however this is a task which have been fascinated many mathematicians. In this work we present some historical information and properties of irrational, algebraic and transcendental numbers. The main part of this work are the proofs of irrationality and transcendence of the numbers e and π. We have noticed these two numbers are known by students in high school, but they are never shown as transcendental numbers. We believe that it is possible to present the notion of transcendental and algebraic numbers for the students, at least superficially. For instance, it is possible to explore the notions of infinite, cardinality, among others and also the rich history of these kind of numbers.