Visualization of finite groups: The case of the Rubik's cube and supporting properties in GeoGebra
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...
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| Format: | Article |
| Language: | English |
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Muhammadiyah University Press
2024-10-01
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| Series: | Journal of Research and Advances in Mathematics Education |
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| Online Access: | https://journals2.ums.ac.id/index.php/jramathedu/article/view/5516 |
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| author | Renata Teófilo de Sousa Francisco Régis Vieira Alves Ana Paula Aires |
| author_facet | Renata Teófilo de Sousa Francisco Régis Vieira Alves Ana Paula Aires |
| author_sort | Renata Teófilo de Sousa |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ba3821a8fded4b4694ccbacab7e8a7ac |
| institution | OA Journals |
| issn | 2503-3697 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Muhammadiyah University Press |
| record_format | Article |
| series | Journal of Research and Advances in Mathematics Education |
| spelling | doaj-art-ba3821a8fded4b4694ccbacab7e8a7ac2025-08-20T02:36:12ZengMuhammadiyah University PressJournal of Research and Advances in Mathematics Education2503-36972024-10-0124826110.23917/jramathedu.v9i4.55165534Visualization of finite groups: The case of the Rubik's cube and supporting properties in GeoGebraRenata Teófilo de Sousa0https://orcid.org/0000-0001-5507-2691Francisco Régis Vieira Alves1https://orcid.org/0000-0003-3710-1561Ana Paula Aires2https://orcid.org/0000-0001-8138-3776Department of Education of the State of CearáFederal Institute of Education, Science and Technology of CearáUniversity of Trás-os-Montes and Alto DouroIn 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.https://journals2.ums.ac.id/index.php/jramathedu/article/view/5516rubik's cubegroup theorypermutation groupsgeogebra |
| spellingShingle | Renata Teófilo de Sousa Francisco Régis Vieira Alves Ana Paula Aires Visualization of finite groups: The case of the Rubik's cube and supporting properties in GeoGebra Journal of Research and Advances in Mathematics Education rubik's cube group theory permutation groups geogebra |
| title | Visualization of finite groups: The case of the Rubik's cube and supporting properties in GeoGebra |
| title_full | Visualization of finite groups: The case of the Rubik's cube and supporting properties in GeoGebra |
| title_fullStr | Visualization of finite groups: The case of the Rubik's cube and supporting properties in GeoGebra |
| title_full_unstemmed | Visualization of finite groups: The case of the Rubik's cube and supporting properties in GeoGebra |
| title_short | Visualization of finite groups: The case of the Rubik's cube and supporting properties in GeoGebra |
| title_sort | visualization of finite groups the case of the rubik s cube and supporting properties in geogebra |
| topic | rubik's cube group theory permutation groups geogebra |
| url | https://journals2.ums.ac.id/index.php/jramathedu/article/view/5516 |
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