Estudo sobre o cálculo de áreas e volumes utilizando o Método de Exaustão e o Princípio de Cavalieri

• Ano de defesa: 2013
• Autor(a) principal: Lima, Francisco do Nascimento
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Mestrado Profissional em Matemática; UFPB
• Palavras-chave em Português: Áreas; Areas; Volumes; Método de exaustão; Princípio de Cavalieri; Method of Exhaustion; Cavalieri principle; MATEMATICA::MATEMATICA APLICADA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/7518

This study aimed to demonstrate some mathematical formulas used in geometry to serve as a reference source for teachers and students of Basic Education. We have begun with some of the great thinkers of Ancient Greece and with a discussion of the History of Geometry since its rst days in order to understand its emergency and development. We, then, have showed that the measure of a segment is a real number, that the length of a circle is proportional to its radius and that the area of a circle is proportional to the square of its own radius. We also demonstrated that same-area polygons can be equally decomposed. In the end of this study we did obtain the formulas on how to calculate the volume of some geometric solids using the exhaustion method and Cavalieri principle.