Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino

Abstract

This study has as main theme the use of digital technologies to teach geometry. The objective is to show how a classroom approach can be favorable to the teaching of this discipline and for that reason the geometric constructions in the Geogebra program have been taken as object of study. Initially it was proposed a theoretical survey that would support the study, guiding the way in which the work would develop. After a brief presentation of the program Geogebra, was developed the construction of some geometric figures, detailing its main characteristics and results, also showing a guide for its construction in the program. The proposed figures were the notable points of a triangle (barycentre, orthocenter, incenter and circumcenter), Euler’s straight line, the nine-point circle, the platonic solids (tetrahedron, hexahedron or cube, octahedron, dodecahedron and icosahedron), and the archimedean solids (truncated tetrahedron, truncated dodecahedron, truncated icosahedron, snub cube, cuboctahedron, dodecahedron snub, icosidodecahedron, rombicuboctahedron, great rombicuboctahedron, rhombicosidodecahedron and large rhombicosidodecahedron). These constructions served for the final step of this work which was an experiment of teaching involving students of the 8th and 9th year of the private school system. The experiment consisted of three stages, the first being done in the classroom using paper, rubber, ruler, compass and protractor, the second using the program and the third comparing the previous two steps. During the experiment, the geometric construction and the teaching possibilities were emphasized and one of the main results obtained indicated that Geogebra was well accepted and that all the students expect to work with it again, because it makes the geometry more accessible until for those who say they have no affinity with this discipline. Another result observed is how to use this didactic resource in the classroom, since it was well accepted and showed positive results in teaching.