A curricular application: the game of parallel

Abstract

The Game of the Parallel is a practice result of a study of the Desargues’s theorem and Fagnano’s and Malfatti’s problems, using different geometries, which is included in a master’s degree for teachers. Recognizing the potential that the game may have in context of the classroom and outside it, the creation of a game was, from the beginning, the way chosen to, in some way, fit the content explored in this work. The Game of the Parallel was born from the union of geometric element common to the three problems studied, the triangle, with the concept that distinguishes the geometries are addressed in their studying, the concept of parallelism, which allows you to make the distinction between the euclidian geometry and non euclidean geometries. In this regard, the main parts of the game are equilateral triangles. Its creation was inspired in the problem of Fagnano, because in each one of them, is inscribed an orthic triangle. The concept of parallelism is present throughout the development of the game, through the construction of straight line segments that are strictly parallel. One of the purposes present at the creation of the game is related to the fact that this has the possibility to be used in classroom context. Thus, the combination between the experience of teaching during the third cycle of Basic Schooling and the nature of work here developed, was born the game of Parallel.