O uso do teorema de Pick no ensino de geometria e na resolução de problemas de olimpíadas

Abstract

The object of study of this academic work is to discuss how the Pick's theorem can be applied in the teaching of geometry, either in a traditional way or with the use of technological resources, and in solving mathematical Olympiad problems. Therefore, a bibliographic research will be carried out with the objective of finding articles and books that address the subject and that can be used as a reference in the elaboration of didactic activities, identifying the various applications of Pick's theorem. In addition, a didactic sequence will be developed for a class in Middle School, encompassing a geometry content (where Pick's theorem will be used), with the entire sequence based on the National Common Curricular Base (BNCC), the National Curriculum Parameters (PCN), Souza (2021), Sé (2016), and other authors who discuss the theme so that teachers can effectively use Pick's theorem in their classes. Another approach that will be explored is the solving of questions from the Brazilian Mathematics Olympiad for Public Schools (OBMEP), using Pick's theorem. Questions that allow for demonstrating the practical application of the theorem will be selected, in order to encourage its use in the classroom. To aid in the visualization process of the network of points on the plane, or grid mesh, and geometric figures, the GeoGebra software will be used. This will allow for the creation of precise drawings and facilitate the demonstration of the applications of Pick's theorem in didactic activities. The research of OBMEP questions and the use of the GeoGebra software will be important tools to make the learning of the subject more dynamic and practical. It is expected that this work will contribute to the improvement of the teaching of plane geometry and to the development of students' skills in this area of knowledge.