State of the art on the Leonardo sequence: An evolutionary study of the epistemic-mathematical field

Abstract

This work is a segment of an ongoing doctoral research in Brazil. The Leonardo numbers and the Leonardo sequence have gained attention from mathematicians and the academic community. Despite being a relatively new sequence within mathematical literature, its discussion has intensified over the past five years, giving rise to other branches, with contributions and associations to other topics in mathematics. Thus, the aim of this study was to construct and present the state of the art of the Leonardo sequence, considering its historical aspects and highlighting works on its evolutionary process in the epistemic-mathematical field, regarding its generalization, complexification, hyper complexification, and combinatorial model during the last five years (2019-2023). The methodology used was a bibliographic study, where the state of the art was carried out through the mapping of publications on the subject. Twenty-four research works related to the key descriptors “Leonardo sequence”, “Leonardo numbers”, “complexification”, “generalization”, “hybrids”, and “combinatorial model” were found, cataloged, and discussed. From the analysis of these studies, it is noted that its development in pure mathematics has advanced to other branches and discoveries, and that, albeit timidly, research on the subject has emerged directed towards the field of education, especially in the initial teacher training and, particularly, in Brazil.