Research on the group theory based on the perspective of the Rubiks Cube

Abstract

With the development of mathematics, more and more fields of study have been created and progressed, it is worth to implement the knowledge into the real life. There is a well-known puzzle called the Rubiks Cube, has many connections to a branch of abstract algebra group theory. Therefore, this paper will discuss how the Rubiks Cube showing the properties from group theory, by introducing basic knowledges of group theory, followed by examples in terms of this intelligent toy. This paper will first introduce the properties of the Rubiks Cube, then move to the construction of its group. Subsequently, the four axioms that form a group are explained. After that, the reasons why the operations of the Rubiks Cube are able to form a group are explained as the examples of those four axioms. It is followed by the concepts in group theory, and provisions of the exemplifications in terms of the Rubiks Cube, such as closure, cyclicity, Cayleys graph. Explaining the group theory from the perspective of the Rubiks Cube provides a tangible channel to learn the intangible knowledges effectively. Learners are able to study these hard knowledges easily by rotating a simple toy and observing the conclusions.