Um breve estudo da sequência de Fibonacci usando recorrências e geometria: uma aplicação no ensino básico

Abstract

In this dissertation we study, recurrences first order linear as well as recurrences second order linear lines and some of their properties. We introduce the Sequence of Fibonacci its terms, which we will call the Fibonacci Numbers, we also study some important properties, namely one of them whose name is Binet Formula. We verify that the limit of the ratio between the (n + 1)-th and the n-th Fibonacci Number is equal to the Gold Number. Then we study an important relationship of the Sequence of Fibonacci in geometry with respect to the Golden Number, the what is the solution to a problem posed by Euclid in Elements. We try to mediate the teaching of the Sequence of Fibonacci in elementary school, through an activity guided tour.