Articulação entre Sequências Recursivas e teoria dos Grupos Finitos
o caso da Sequência de Padovan
DOI:
https://doi.org/10.33871/rpem.2024.13.31.9228Abstract
This article aims to present an approach to explore the Padovan sequence in conjunction with finite group theory in the context of mathematics education. To this end, we adopt the Didactic Engineering as research methodology, in its first two phases - preliminary analyses and conception and a priori analysis -, combined with the Theory of Didactic Situations, to compose a teaching model. We used the GeoGebra software as support, where we relate the Padovan sequence, which is an infinite sequence, to finite groups through modular congruence, rewriting it as a finite sequence. From the construction and its analysis, it was possible to visualize the behavior of the Padovan sequence modulo m, revealing cyclical patterns in the sequence that can be interpreted as elements of finite groups. We discuss how these results can be applied in the classroom in an approach to teaching concepts of finite groups and numerical sequences, in an associated and meaningful way.Downloads
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