O surgimento da Trigonometria: os métodos de Hiparco e Ptolomeu na construção das primeiras tabelas trigonométricas - Silva, Thiago Aparecido da (Universidade Federal do Tocantins, 2024)
Trigonometry is an important branch of Mathematics, which has been used since the beginning of its creation as an aid to Astronomy. This work presents a study of the works of two mathematicians of antiquity, Hipparchus and Ptolemy. Aiming to analyze the methods used bythem in the construction of their Tables of Chords and to make a historical survey of these tworesearchers. To this end, a bibliographic and descriptive research was carried out to acquire the necessary knowledge for the object of study and answer the research question: “what were the steps and methods adopted in the early days of these studies, by Hipparchus and Ptolemy, for the construction of your Tables of Chords?”. It was found that Hipparchus methods give rise toa Table of Chords, which is related to the current trigonometric table. While Ptolemy’s methods, give rise to a more complete Table of Chords than that of Hipparchus. We sought to understand the methods used in the constructions, analyzing the historical context and applications, in addition to the mathematical production itself. These Tables were important for several areas of science, presenting everyday applications, which contributed to the development of societies. From these results we can understand how one of the steps that were the basis for Trigonometry occurred, and with that to understand that it had its development in a gradual way