Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 9, 13 November 2023
Open
Access | Article
Research on the group theory based on the perspective of the Rubik’s Cube
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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 Rubik’s Cube, has many connections to a branch of abstract algebra – group theory. Therefore, this paper will discuss how the Rubik’s 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 Rubik’s 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 Rubik’s 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 Rubik’s Cube, such as closure, cyclicity, Cayley’s graph. Explaining the group theory from the perspective of the Rubik’s 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.
Keywords
Rubik’s Cube, Group Theory, Cyclic Group, Cayley’s Graph
References
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3. Chen J J 2004 Group theory and the Rubik’s cube. JHU Press.
4. Hu W T 2023 Applying the Group Theory to Rubik’s Cube. Highlights in Science, Engineering and Technology, 47, 122-125.
5. Rokicki T, et al. 2013 The Diameter of the Rubik's Cube Group Is Twenty. SIAM J. Discret. Math., 27, 1082-1105.
6. Anderson D 2023 Let’s Make Patterns: Symmetric Rubik’s Cube Permutations. Working paper.
7. Daniels L 2014 Group theory and the Rubik’s Cube. Lakehead University.
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Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
- ISBN (Print)
- 978-1-83558-129-2
- ISBN (Online)
- 978-1-83558-130-8
- Published Date
- 13 November 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/9/20240734
- Copyright
- 13 November 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited