Número de ouro: uma viagem pela história e aplicações

Abstract

This work addresses the golden ratio, exploring its historical context, its mathematical definitions, and some of its applications. The research begins with the conceptualization presented by Euclid, through the extreme and mean ratio, and with the contribution of Fibonacci, whose ratio between consecutive terms of the numerical sequence approximates the golden ratio. In addition to the historical review, the study examines the presence of the golden ratio in geometric figures, such as the rectangle, the pentagram, and the golden spiral, as well as the "algebraic juggling" that establishes false relationships between the construction of historical monuments and this irrational constant. The work also investigates its occurrence in nature, such as in the arrangement of leaves and the formation of galaxies, and in artistic and architectural applications, ranging from classical buildings to works by artists Leonardo da Vinci and Salvador Dalí. This research is characterized as bibliographic, following the methodology of Gil (2002), based on books, scientific papers, and dissertations that discuss the relevance of the golden ratio in mathematics and in areas where it is applied. The conclusion is that the golden ratio, besides having great historical and aesthetic significance, reveals a connection between mathematical theory and natural and cultural manifestations, allowing for a critical understanding of its importance and the associations attributed to it.