Um estudo do liber quadratorum (1225) de Leonardo Fibonacci (1180 – 1250) e suas potencialidades para o ensino de matemática

Abstract

In this research report we show the Italian mathematician Leonardo de Pisa, better known as Fibonacci, who we refer to as Leonardo Fibonacci, who contributed significantly to the mathematical community of his time, attracting attention from important people of this period such as King Frederick II, and to his invitation Leonardo Fibonacci participates of a mathematical tournament, which, as a follow up the construction of his fourth work (that we have known) the Liber Quadratorum. In this way the following question occurs to us: what are the didactic / pedagogical potentialities that can be evidenced from these propositions and their demonstrations that can be used in the classroom to effect the teaching / learning of mathematical contents? In order to answer this question, we aim in this research report to analyze the problems contained in Leonardo Fibonacci 's Liber Quadratorum, in which we aim at a better understanding of the concepts, providing a material in Portuguese and searching for possible didactic / pedagogical potentials. To do so, we searched for materials that subsidized the study and a basic text for the construction of the material in Portuguese referring to twelve propositions contained in the Liber Quadratorum, which deal with the sequence of consecutive odd numbers and square numbers. The book of squares of LE Sigler of 1987, as our main reference and BR McClenon in his work titled Leonardo of Pisa his Liber Quadratorum of 1919 as our secondary reference. We took a tour of the period experienced by this important character, who was a teacher and wrote about mathematics, so we highlight its influence for the development and dissemination of algorithmic methods of Arab mathematics in Europe in the early thirteenth century, from a proposed model diagram by Chaquiam (2015, 2016), thus, a basis was built so that we could point out the didactic / pedagogical potentialities of this book by Leonardo Fibonacci, especially considering the reinforcing arguments of Miguel (1997) and Miguel and Miorim (2004). After the analysis, it was possible to respond to our questioning and we could point out potentialities such as: construction of several ways to find the Pythagorean triples, potentiation activities, mainly squares, activities with square root, among others described in this report. In this way, to maintain the Liber Quadratorum for explicitly pedagogical purposes, by vectorizing the teaching, can greatly assist the mathematical educator who wants to trace paths that meet the needs of the student.