Visualization and properties of boards and tiles: The case of the Padovan or Cordonier sequence

Francisco Alves; Renata Vieira; Paula Catarino; Milena Mangueira

doi:10.29333/mathsciteacher/16858

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Francisco Alves ¹ ^* , Renata Vieira ² , Paula Catarino ³ , Milena Mangueira ¹

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¹ Federal Institute of Education, Science and Technology of the State of Ceará – IFCE, BRAZIL² Federal University of Ceará - UFC, BRAZIL³ University of Trás-os-Montes and Alto Douro – UTAD, PORTUGAL^* Corresponding Author

Abstract

The study of recurring numerical sequences usually involves a restricted context of circulation and communication of new ideas and abstract mathematical properties. On the other hand, authors of the history of mathematics books tend to emphasize, in an almost restrictive way, anecdotal curiosities about the Fibonacci sequence. Given this context, in this work, we find a proposal for exploring arithmetic and combinatorial properties using the notion of board and tiles, which correspond to properties of the Padovan or Cordonier numerical sequence. Through some elements, we will demonstrate that such an approach involves potential for application in the classroom to provide a relevant role for visualization and learning.

Keywords

number sequences
board and tiles
Padovan or Cordonier
mathematics teacher
visualization

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

Journal of Mathematics and Science Teacher, Volume 5, Issue 4, 2025, Article No: em086

https://doi.org/10.29333/mathsciteacher/16858

Publication date: 01 Oct 2025

Online publication date: 03 Sep 2025

Article Views: 120

Article Downloads: 34

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How to cite this article

APA

Alves, F., Vieira, R., Catarino, P., & Mangueira, M. (2025). Visualization and properties of boards and tiles: The case of the Padovan or Cordonier sequence. Journal of Mathematics and Science Teacher, 5(4), em086. https://doi.org/10.29333/mathsciteacher/16858

Vancouver

Alves F, Vieira R, Catarino P, Mangueira M. Visualization and properties of boards and tiles: The case of the Padovan or Cordonier sequence. Journal of Mathematics and Science Teacher. 2025;5(4):em086. https://doi.org/10.29333/mathsciteacher/16858

AMA

Alves F, Vieira R, Catarino P, Mangueira M. Visualization and properties of boards and tiles: The case of the Padovan or Cordonier sequence. Journal of Mathematics and Science Teacher. 2025;5(4), em086. https://doi.org/10.29333/mathsciteacher/16858

Chicago

Alves, Francisco, Renata Vieira, Paula Catarino, and Milena Mangueira. "Visualization and properties of boards and tiles: The case of the Padovan or Cordonier sequence". Journal of Mathematics and Science Teacher 2025 5 no. 4 (2025): em086. https://doi.org/10.29333/mathsciteacher/16858

Harvard

Alves, F., Vieira, R., Catarino, P., and Mangueira, M. (2025). Visualization and properties of boards and tiles: The case of the Padovan or Cordonier sequence. Journal of Mathematics and Science Teacher, 5(4), em086. https://doi.org/10.29333/mathsciteacher/16858

MLA

Alves, Francisco et al. "Visualization and properties of boards and tiles: The case of the Padovan or Cordonier sequence". Journal of Mathematics and Science Teacher, vol. 5, no. 4, 2025, em086. https://doi.org/10.29333/mathsciteacher/16858