Visualization of finite groups: The case of the Rubik's cube and supporting properties in GeoGebra
DOI:
https://doi.org/10.23917/jramathedu.v9i4.5516Keywords:
Rubik's cube, Group Theory, Permutation Groups, GeoGebraAbstract
In this text, we present a discussion about the Rubik's Cube and its relationship with Group Theory, particularly permutation groups, as well as possibilities for exploring it using the GeoGebra software interface. We bring a brief discussion about the concept of group, aspects of the Rubik's cube, the Rubik's group as a group of permutations and possibilities for its exploration in GeoGebra. Based on this study, we recognize the potential to delve into permutation groups in Abstract Algebra through a visual interface that associates their properties with a tangible and manipulable object. Additionally, there is the potential for simulating their movements using Dynamic Geometry software, such as GeoGebra. These findings highlight the relevance of GeoGebra as a useful tool for visualizing and understanding permutation groups, promoting a more intuitive and accessible approach to Group Theory in the educational context.
References
Alves, F. R. V. (2019). Visualizing the Olympic Didactic Situation (ODS): Teaching mathematics with support of the GeoGebra software. Acta Didactica Napocensia, 12(2), 97-116. https://doi.org/10.24193/adn.12.2.8
Alves, F. R. V. (2022). Didactic Engineering (DE) and Professional Didactics (PD): A Proposal for Historical Research in Brazil on Recurring Number Sequences. The Mathematics Enthusiast, 19(1). https://doi.org/10.54870/1551-3440.1551
Bandelow, C. (1982). Inside Rubik’s cube and beyond. Birkhäuser Boston.
Carter, N. C. (2009). Visual Group Theory. Bentley University.
Chen, J. (2004). Group Theory and the Rubik’s Cube. (Lecture notes). Texas State Honors Summer Math Camp.
Davis, T. (2006). Group Theory via Rubik’s Cube. Class notes. Available at: https://docplayer.net/252967-Group-theory-via-rubik-s-cube.html
Davvaz, B. (2021). Groups and Symmetry: theory and applications. Springer. https://doi.org/10.1007/978-981-16-6108-2
Garcia, A., & Laquin, Y. (2002). Elementos de Álgebra. Projeto Euclides. IMPA.
Gonçalves, A. (1995). Introdução à Álgebra. Projeto Euclides. IMPA.
Joyner, W. D. (1997). Mathematics of the Rubik’s cube. Faculty of Physics, University of Warsaw.
Joyner, W. D. (2008). Adventures in Grout Theory: Rubik’s Cube, Merlin’s Machine, and other Mathematical Toys. The Johns Hopkins University Press.
Monteiro, A. T. M., Moura, L. F. C. M. & Fonseca, R. V. (2019). Grupos Diedrais: uma proposta concreta para uma apresentação inicial da Álgebra Abstrata para licenciandos em Matemática. Revista Matemática e Ciência: conhecimento, construção e criatividade, 2(2), 56-86. https://doi.org/10.5752/P.2674-9416.2019v2n2p56-85
Romero, R. E. (2013). Las matemáticas del cubo de Rubik. Revista Pensamiento Matemático, 3(2), 97-110.
Travis, M. (2007). The Mathematics of the Rubik's Cube. University of Chicago.
Schültzer, W. (2005). Aprendendo Álgebra com o Cubo Mágico. V Semana da Matemática da UFU. UFSCar.
Vágová, R., & Kmetová, M. (2018). The Role of Visualisation in Solid Geometry Problem Solving. Proceedings of 17th Conference on Applied Mathematics, Bratislava, pp. 1054-1064.
Warusfel, A. (1981). Réussir le Rubik’s cube. Éditions Denöel.
Wussing, H. (1984). The Genesis of the Abstract Group Concept. Dover Books on Mathematics.
Zazkis, R; Dubinsky, E., & Dautermann, J. (1996). Coordinating visual and analytic strategies: a study of students’ understanding of the Group D4. Journal for Research in Mathematics Education, 27(4), 435-457. https://www.jstor.org/stable/749876
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Copyright (c) 2024 Renata Teófilo de Sousa, Francisco Régis Vieira Alves, Ana Paula Aires
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