Razão áurea: abordagem histórica, aplicações e sua relação com Fibonacci

Abstract

This dissertation aims to conduct a study on the Gold Number, also called Golden Ratio, a number that has impressed many researchers throughout history for its numerous applications in daily life. Initially the definition is presented algebraic theory of the Golden Ratio, some of its properties and its intrinsic relationship with Fibonacci sequence. Through a historical approach we present numerous Golden Reason applications in Architecture, Botany, the human body and also within the mathematics itself, more specifically, in Geometry. At the end of the work, a analysis of issues in Vestibular and Enem that involve this concept, thus emphasizing the importance of these themes in basic education as an opportunity to awaken in students a new way of thinking about mathematics as a science that changes society. In addition to this we suggest some activities that comprise the Golden Number, associating it with geometric constructions, other areas of mathematics and even some curiosities.