O uso de coordenadas baricêntricas com algumas aplicações reais

Abstract

The present dissertation aims to show the use of barycentric coordinates in solving plane geometry problems and their applications in a modern society, a society that increasingly presents the need to present new ways to solve problem situations that appear in everyday life. In this work, we will develop the definition of barycentric coordinates and some of their properties, with emphasis on the study of triangle geometry. The barycentric coordinates of some of the main notable points of the triangle studied in basic education will be demonstrated, the equation of lines through these coordinates, as well as the demonstration of parallelism and perpendicularity between lines with the preface of a new concept through the introduction of point at infinity, and there will also be a demonstration of the intersection of two lines and how to calculate the distance between two points using these coordinates. Then we will talk about the use of barycentric coordinates in solving some geometry problems and their applications in society. Finally, we will discuss the possibility of inserting this content in basic education, as well as the possibility of deepening it in the computational area.