A sequência de fibonacci e o número de ouro e suas aplicações na arte e arquitetura

Abstract

The present work has as purpose the study of the Fibonacci sequence and the golden number and its application in the field of arts and architecture. The justification for choosing this topic is due to its contribution to Algebra and for having several applications of its theory in various fields, such as the focus of our work in Art and Architecture, so that they learn the theory and its practical application. Thus, we sought to answer the following question: What are the applications of the Fibonacci sequence related to the golden number, used in works of art and construction? We described the history of Fibonacci and the problem he solved about the reproduction of rabbits, giving rise to the Fibonacci numbers and sequence. We present the demonstrations of the properties of the sequence and the powers of the golden number. We show the definitions of the golden ratio and the geometric constructions of the golden rectangle and the golden triangle until it forms the golden spiral, known as the Fibonacci spiral, and we also define the regular pentagon and the pentagram. This is bibliographic research of materials such as books, articles, monographs, and dissertations. Analyzing the applications in architectural projects from antiquity to the present day, in the paintings of great artists, present in music and photographs.