Construções geométricas com régua e compasso e os três problemas clássicos da Matemática grega

Abstract

Geometric constructions with ruler and compass are excellent tools to develop in elementary and high school students, both creativity and artistic skills, and the consequent geometric vision, so necessary to solve problem situations in our daily lives. However, in recent years, such constructions have not received the proper importance and emphasis in teaching materials. Thinking about this, we bring in this work the proposal to serve both students in elementary and high school as well as teachers who teach these segments, presenting in a simple and direct way several constructions that are important for student development within the Geometry. One of the motivating elements of this work is precisely to try to fill this gap in the educational environment: the construction with ruler and compass. To this end, several figures were presented, bringing a step-by-step from its constructions, ranging from basic geometric concepts to some activities that stimulate the creativity. Thus, it is a work that aims to show students how geometric construction is done and, at the same time, presenting justifications for the constructions. For teachers, there is a chapter further developed, bringing a support for theory based on algebraic concepts. With the use of such tools, the insolubility of the three classical problems of Greek mathematics that for centuries intrigued mathematicians is presented and proven. Such problems are: the doubling of cube, the squaring of circle, and the 60º angle trisection. Finally, we present a working proposal to be developed in the classroom that shows how some well-known figures can be constructed using only the ruler and compass.