Author:
Alves Francisco Régis Vieira, ,Pinheiro Carla Patrícia Souza Rodrigues,de Sousa Renata Teófilo,Catarino Paula Maria Machado Cruz, , ,
Abstract
"This article is an excerpt from a master's thesis developed in Brazil, in which we approach recurrent and linear sequences, given some intriguing particularities in their definitions and the scarcity of discussion of this topic in the literature of the History of Mathematics, especially with regard to its geometric representation. Thus, we aim to present the identities of Fibonacci, Lucas, Jacobsthal and Padovan in a three-dimensional visualization with the contribution of GeoGebra software. The research methodology chosen was bibliographical, exploratory in nature, where we have theoretical support in works such as Oliveira and Alves (2019), Silva (2017), Souza and Alves (2018), Vieira and Alves (2020). This research brings as results a set of geometric constructions of the identities of the proposed sequences, in three-dimensional perspective, being a support for future works developed around this theme. GeoGebra was essential in the process of constructing and visualizing the sequences, as it provided strategies for understanding the recurrence relations and the properties of the Fibonacci, Lucas, Jacobsthal and Padovan sequences, through the behavior of the visual representations of these identities."
Subject
General Agricultural and Biological Sciences
Reference30 articles.
1. "1. Alves, F. R. V. (2017). Didactic Engineering for Jacobsthal's Generalized s-Sequence and Jacobsthal's (s,t)-Generalized Sequence: preliminary and a priori analyzes [Engenharia Didática para a s-Sequência Generalizada de Jacobsthal e a (s,t)-Sequência Generalizada de Jacobsthal: análises preliminares e a
2. priori]. Revista Iberoamericana de Educación Matemática, 51, 83-106. http://funes.uniandes.edu.co/17151/1/Vieira2017Engenharia.pdf
3. 2. Alves, F. R. V. (2022a). Fibonacci, Tribonacci, etc. sequences and the boards [A Sequência de Fibonacci, Tribonacci, etc. e tabuleiros]. Boletim GEPEM (Online), 80, 311-323. DOI: 10.4322/gepem.2022.055
4. 3. Alves, F. R. V. (2022b). Combinatory properties about the Jacobsthal sequence, the notion of the board and some historical notes [Propriedades Combinatórias sobre a sequência de Jacobsthal, a noção de tabuleiro e alguns apontamentos históricos]. Revista Cearense de Educação Matemática, 1, 1-13. DOI: 10.56938/rceem.v1i1.3146
5. 4. Alves, F. R. V., Vieira, R. P. M., Silva, J. G. & Mangueira, M. C. S. (2019). Didactic Engineering for teaching the Padovan sequence: a study of the extension to the field of integers [Engenharia Didática para o ensino da sequência de Padovan: um estudo da extensão para o campo dos números inteiros]. In: Gonçalves, F. A. M. (Ed.). Science Teaching and Mathematics Education [Ensino de Ciências e Educação Matemática]. chapter 2. Atena Editora.