Contagem de figuras: resgatando a simplicidade e a beleza do pensamento matemático

Abstract

In this work, the theme counting of figures was developed, specifically, in situations involving counting of points, segments, paths and regions represented by flat figures. A diversity of contexts that exploit the theme have facilitated the use of Mathematics contents found in Algebra, Arithmetic and Geometry. Some counting methods were presented with the purpose of improving strategies, observation capacity, speed of reasoning and precision in the counting process. Throughout the work, care was taken to present problems whose figures aroused the need and curiosity to tell. Most of these problems were taken from Andr´asz Szil´ar’s Elementary Combinatorial Geometry, an assistant professor at the Babes-Bolyai University in Cluj Napoca, Romania, and from the book Counting Eulerian Tour Figures, which is part of the Mathematical Reasoning collection by Adolfo Povis Vega . There are also in this study questions from the tests of the access examination to the PROFMAT, the ENA, whose approach compares the official solutions with the techniques and methods that are the subject of this writing, aiming to broaden students’ repertoire in solving problems. Next, a didactic sequence was presented as a proposal of introduction to the study of Arithmetic Progression and Combinatorial Analysis, planning, through teaching practices, to rescue the simplicity and beauty of mathematical thinking.