Curiosidades da sequência de Fibonacci e da sequência de Padovan : investigações inusitadas

Abstract

In this master's thesis will be presented curious facts about numeric sequences of Fibonacci and Padovan, which are recursively. Starts with an sequence definition's making a historical rescue of Fibonacci number's and Padovan number's presenting many of yours aplications and curiosities, also doing an historical contextualization of creators life's of this sequences. Also, will be defined some proprieties of linear recurrences by Ist, 2nd, 3rd and any order. Will be affirmed and discussed two algebric discoveries; first envolving of areas a quarter of a circle found in the spiral created by Fibonacci numbers and a another about a equilateral triangles areas found in a spiral created by Padovan numbers. Will be approach which are directions for basic education about recursive numbers sequences or no recursives and there will be comment about how it is approached in the basic education.