Geometria e trigonometria aplicadas na topografia: uma alternativa para a interdisciplinaridade e a contextualização

Abstract

The present work aims to introduce the mathematical contents of the first year of high school in an interdisciplinary way, relating them to topics of topography. The first chapter presents some fundamental concepts of Topography and several historical instruments used for topographic measurements. The second chapter begins with an analysis of first-year high school textbooks and the topographical applications contained in them, and continues to describe the contents of geometry and trigonometry along with many applications in Topography. Finally, the third chapter presents some fundamental procedures of Topography, which do not fit into a single mathematical content, seeking to justify them mathematically. The work aims to bring the most relevant demonstrations, examples and applications in all contents presented, offering the teacher and the students an alternative for contextualization in the Topography for the presented mathematics. It is intended, with this, to show that geometry and trigonometry, sometimes uninteresting and meaningless to students, can solve problems in real situations, which are useful and interesting. In addition to the work, a didactic theodolite for 3D printing, available free on the Internet, and a Handbook of Theodolite Use in Mathematics Classrooms were developed.