Construção de Polígonos Regulares com o Geogebra: Evidenciando a Essência do Hexágono e do Pentágono

Abstract

The objective of this research is to build geometric objects using the GeoGebra software in order to create investigative activities with mathematical objects involving regular polygons, more specifically the regular pentagon and hexagon. The question that guided the investigation was: How to build geometric objects that intend mathematical objects through the GeoGebra software? The research question guided the constitution and analysis of data, showing that the principles of geometric constructions with ruler and physical compass can be applied in GeoGebra. The research has Edmund Husserl's Phenomenology as theoretical foundation and commentators of the philosopher, such as Ales Bello (2006) and Sokolovski (2004). Assuming a phenomenological approach, using epoché, eidetic reduction and imaginative variation, we established a method that allowed the constitution and analysis of research data and thus determine and carry out the construction of geometric objects that intend mathematical objects for the determination of the essence and the explanation of your identity. As a result of research, we determined the importance of elaborating a construction protocol for geometric objects and carrying out instructions in GeoGebra, so that we could carry out the investigations. We realize that the unveiling of the essence and the explanation of the identity of the geometric objects are important to be sure which geometric object is intending the intended mathematical object. The essence of the regular hexagon and pentagon is to have congruent sides and angles, so we have a coexistence of attributes in the essence of these geometric objects; to approach the identity, we need to treat the analyzed objects in the general category regular polygons. Thus, we explain that their identity is to be convex, but we can also speak of the identity of each one individually, which will converge to the regularity of the mathematical objects that we are intending in the transcendental dimension