Polígonos e poliedros equidecomponíveis

• Ano de defesa: 2018
• Autor(a) principal: Fernandes, Flavia Mescko
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Tecnológica Federal do Paraná; Curitiba; Brasil; Programa de Pós-Graduação em Matemática em Rede Nacional; UTFPR
• Palavras-chave em Português: Bolyai, Farkas, 1775-1856; Hilbert, David, 1862-1943; Wallace, William, 1768-1843; Demonstração automática de teoremas; Polígonos; Poliedros; Isometria (Matemática); Geometria; Matemática - Estudo e ensino; Professores de matemática; Matemática; Automatic theorem proving; Polygons; Polyhedra; Isometric (Mathematics); Geometry; Mathematics - Study and teaching; Mathematics teachers; Mathematics; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.utfpr.edu.br/jspui/handle/1/2972

We show in this work the Wallace-Bolyai-Gerwien theorem and Hilbert’s third problem. We use the first to proof by equicomposition the area of plane geometric figures and the second to show that the demonstration of relations for volumes can not always be done by equicomposition. Also, we have analyzed some textbooks of Basic Education to evaluate how much equicomposition is used to establish relations for areas and volumes. We also suggest ludic-manipulative activities for Elementary and High School by exploring the equicomposition in two and three dimensions.