Grupos de simetria dos polígonos regulares: da teoria à ampla possibilidade de aplicações

Abstract

This research project aims to explore the study of the symmetry group of regular polygons. polygons. This investigation is based on understanding and classifying algebraic structures, resulting in definitions and properties that are applicable in various areas. From this, the symmetry group of regular polygons and its properties can be developed. Our objectives were to generalize the main relations of this group and their applicability. In this way, the research was divided into stages that explored aspects such as historical context, theoretical foundations, demonstrations, examples and applications. The choice aims to enrich the existing literature, especially by means of a practical application in conservation theory. conservation theory, highlighting the relevance of this research. Authors such as Évariste Galois and Felix Klein, advocates of group theory, influenced the choice of topic. the topic. The paper addresses the practical application of symmetry in conservation theory, exemplifying how symmetry is essential for the flight of a drone. The proposal is to defend Klein's theory on the broad applicability of symmetry and the importance of algebraic algebraic conceptualization in this investigation. However, it was possible to use algebraic and physical aspects, together with engineering authors, to explain an idealized model of drone flight. drone flight model. In this way, generalizations are made that meet the objectives of the research. Keywords: Group, symmetry, polygons