A proporção áurea e a sequência de Fibonacci

Abstract

Given the amount of erroneous material available, this paper aims to act as a guide and mediator, providing reflections on the Golden Ratio and the Fibonacci Sequence, in order to warn the reader about errors and challenge famous fallacies. This is a bibliographical research carried out on printed material and material available on the internet, seeking impartiality when verifying different points of view. Some myths and truths about the presence and use of the Golden Ratio in famous works and historical monuments will be presented, highlighting aspects that confirm or deny its use. It is observed that mathematics is harmonious, and is present in several areas of art and history. However, the need for harmony and the feeling of beauty provided by a mathematical pattern can lead the observer to make erroneous correlations. Thus, the need arises to provide the reader with a critical and impartial view of the subject addressed, presenting its historical-philosophical context and bringing the final reflection that they are interesting and useful mathematical tools, but they are not the only ones and are not universal. Finally, some discussions are presented about the use of the Fibonacci Sequence and the Golden Ratio in the school context, proposing reflections involving aspects of mathematical history and its interdisciplinarity.