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Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-28T12:29:14Z No. of bitstreams: 1 arquivototal.pdf: 800250 bytes, checksum: 42e76ab05ea580b4fd24a3312b9b4212 (MD5) / Made available in DSpace on 2016-03-28T12:29:14Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 800250 bytes, checksum: 42e76ab05ea580b4fd24a3312b9b4212 (MD5) Previous issue date: 2014-08-29 / In this work we present a study of the regular polyhedra, comparing and discussing the concepts and de nitions given in the study of regular polyhedra in textbooks most widely used in Brazilian high schools. We prove the theorem of Euler, we calculate surface areas and volumes of regular polyhedra. Finally, we present some mathematical software that can be used by students and mathematics teachers in the spatial geometry classes as auxiliary material in the teaching and learning of this subject in the classroom. / Neste trabalho apresentamos um estudo sobre os poliedros regulares, comparando e discutindo os conceitos e as de nições que são dadas no estudo dos poliedros regulares nos livros didáticos mais utilizados nas escolas brasileiras de Ensino Médio. Provamos o teorema de Euler, calculamos áreas de superfícies e os volumes dos poliedros regulares. Por m, apresentamos alguns softwares matemáticos que podem ser utilizados pelos alunos e professores de Matemática nas aulas de geometria espacial como material auxiliar no processo de ensino e aprendizagem deste tema em sala de aula.

Title: Platonic and Archimedean solids and their properties in teaching of mathematics at secondary schools Author: Eva Dohnalová Department: Department of Didactics of Mathematics Supervisor: doc. RNDr. Jarmila Robová, CSc. Abstract: This work is an extension of my bachelor work and it is intended for all people interested in regular and semiregular polyhedra geometry. It is a comprehensive text which summarizes brief history, description and classification of regular and semiregular polyhedra. The work contains proofs of Descartes' and Euler's theorems and proofs about number of regular and semiregular polyhedra. It can be also used as a didactic aid in the instruction of regular and semiregular solids at secondary schools. This text is supplemented by illustrative pictures made in GeoGebra and Cabri3D. Keywords: Regular polyhedra, platonic solids, Platon, semiregular polyhedra, Archimedean solids, Archimedes, dulaism, Descartes' theorem, Euler's theorem.