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

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 move...

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Detalles Bibliográficos
Autor: Grimm, Luis Gustavo Hauff Martins [UNESP]
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2016
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:portugués
OAI Identifier:oai:repositorio.unesp.br:11449/144192
Acceso en línea:http://hdl.handle.net/11449/144192
Access Level:acceso abierto
Palabra clave: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
Descripción
Sumario: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.