O Princípio de Cavalieri e suas Aplicações: Áreas e Volumes

• Ano de defesa: 2021
• Autor(a) principal: Machado, Luiza Lucia Mendes da Costa
• 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: Volume; área; Princípio de Cavalieri; subject.br-rjbn; Matemática
• Link de acesso: http://repositorio.ufes.br/handle/10/14724

Mathematics has prestige and stands out for its practical usefulness: the areas of geometry, magnitudes and measures enable man to have a spatial understanding of the world and complement each other. Some geometrical quantities, such as areas and volumes, are the links between these areas of Mathematics and are important concepts, which must be worked with students still in school age. The screen research aims to contribute to the teaching and learning of areas and volumes, providing a theoretical and methodological study on these quantities, based on Cavalieri’s Principle and seeking to deduce formulas for the calculation of areas and volumes for different flat and solid figures geometric, respectively. To this end, a study is initially described on the guidelines present in official documents of Brazilian education regarding the greatness of volume; the concept of volume is contextualized historically, addressing the contribution of several mathematicians, with emphasis on the influence of Cavalieri and his Principle and the concepts of area and volume are defined by proposing, through didactic sequences, processes for deducting formulas for the calculation of these quantities in flat figures and geometric solids - based on Cavalieri’s Principle. In order to promote a more comprehensive study on the quantities and geometric solids, we seek to analyze each type of solid, highlighting its elements, nomenclatures and classifications. In order to highlight the practical usefulness of volumes and the Cavalieri Principle, this research ends with applications for solving various problems. The research also provides mathematical concepts with the necessary rigor, but in an accessible way to high school students.