Métodos para divisão de segmentos, circunferências, áreas e ângulos em partes (quase) iguais usando apenas régua e compasso

Abstract

This study is dedicated to detailing the construction process and divisions of various geometric figures, using an ungraduated ruler and a compass as the primary tools. Both exact constructions and those requiring approximations will be explored. Before starting the constructions, we will approach the curricular recommendations regarding the teaching of geometric constructions and the trajectory of this topic in Brazilian education, from its emergence to the current scenario. Additionally, the text provides a theoretical foundation on he relevance of geometric constructions in the teaching-learning process for student formation. Subsequently, we present the main geometric constructions, from elementary to more complex constructions, detailing the step-by-step procedures and illustrating them with figures made in GeoGebra. Grounded in the principles of plane geometry and algebra, all constructions are accompanied by mathematical justifications, thus ensuring the validity of the results.