A Note on Leonardo’s Combinatorial Approach - Vieira, Renata Passos Machado; Alves, Francisco Regis Vieira; Catarino, Paula Maria Machado Cruz (Journal of Instructional Mathematics, 2023)
The purpose of this research is to carry out a study of Leonardo's combinatorial approach so that it is possible to visualize these numbers through combinatorial interpretation. Thus, research is being developed regarding methods and approaches to linear and recurring sequences, based on the combinatorial study of the Fibonacci sequence. In fact, the Fibonacci sPquence is related to other sequences, one of which is the Leonardo sequence, which has similarities with the Fibonacci numbers according to some researchers in the field. Given this scenario, the present research addresses the combinatorial interpretation of Leonardo's sequence, allowing the definition of Leonardo's combinatorial model, considering the notion of board and bracelets in Lucas' sequence. As research results, the study deals with the integration of sequence content with the area of Combinatorial Analysis, allowing a mathematical advancement of Leonardo's sequence. Furthermore, you can visualize the sequence numbers in front of the tiles. The aspects studied in this research are linked to the teaching of sequences in the History of Mathematics, allowing the teaching of Mathematics.