Segmento áureo: um diálogo com auxílio de régua e compasso

Abstract

The current work originates from a bibliographic research, whose study was based on the analysis of the golden segment of a given segment, in terms of geometric construction, followed by an analytical examination of the ratio between the measures of such segments. To this end, the main objective was to understand the peculiarities of the number resulting from the ratio between the lengths of the portions of a segment divided into average and extreme ratio. The methodology used was done through a deductive process, which had the aid of constructions with a ruler without markings and a compass. In this context, the results are made up of a set of definitions, axioms and theorems that are taken as a basis to prove the veracity of the most relevant statements present throughout the text. With this, it culminated in the identification of a point that divides a generic segment in the intended reason, as well as, in the analysis of the algebraic implications resulting from this division.