Cubo mágico: propriedades e resoluções envolvendo Álgebra e Teoria de Grupos

• Ano de defesa: 2016
• Autor(a) principal: Grimm, Luis Gustavo Hauff Martins [UNESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Rubik's cube; Group theory; Permutation group; Commutators and conjugates; Didatic proposal; Cubo de Rubik; Teoria de grupos; Grupos de permutação; Comutadores e conjugados; Proposta didática
• Link de acesso: http://hdl.handle.net/11449/144192

The Rubik's Cube is one of the most famous puzzle of the world, and generally attracts the attention of many people, especially mathematicians. The challenge, shapes, symmetries and movements induce the idea of being in front of a mathematical object. And we can go further. The actions and movements in the magic cube are elements that meet all the conditions of the structure of a group, as well as relate to a group of permutations. In light of the Group Theory and Permutations groups we will examine some sequences of movements such as commutators and conjugates. There are several algorithms that solve the magic cube and which are easy to obtain, for example, at the Internet. The aim of this dissertation, beyond to show a resolution, is to provide a path beyond simple memorization of an algorithm in order to understand it. Consequently, the justi cation for the possibility of solving a Rubik's Cube is math and not empirical.