Tesselações no ensino de geometria euclidiana

Abstract

A Tessellation the Euclidean plane is a cover of it for figures that fit perfectly with no overlaps or gaps between them, so that the partitioned area is equal to the total size. This paper presents suggestions of flat Euclidean geometry content approach through these tessellations as a more atractive strategy that aims to show how you can make teaching more attractive Euclidean Geometry, motivated by interest in solving problems tessellations. Initially we will make a brief study of basics of flat Euclidean geometry, definition, elements and types of tessellations. Next it is suggested a sequence of three activities that address, in an interdisciplinary way and contextualized flat Euclidean geometry abstract content for elementary and secondary education.The first activity is one of the regular polygons approach through tessellations of the Euclidean plane using only one type of polygon. The activity 2 deals with the study of the possibilities of tessellations of the Euclidean plane using two or more regular polygons. Activity 3 addresses the isometries through the works of Escher, with analysis of some works of this artist and construction of tessellations in Escher style. It is discussed some applications of tessellations in mathematics itself, in nature, in the information theory and the arts.The exploration of abstract geometric concepts using concrete materials in a contextualized, interdisciplinary approach allows students to develop skills necessary skills to its construction as a citizen conscious and active in the environment they live in. It is hoped that this work will significantly contribute to improving quality of mathematics teaching.