Essência de objetos geométricos triangulares construídos com o geogebra.

Abstract

This work aimed to construct geometric objects using the Geogebra software for mathematical investigation activities. The research question that guided the study was: How can geometric objects be constructed in a way that, when moving some of their constituent elements, the constructed object continues to represent the intended mathematical objects? To answer this question, construction protocols were established, making it possible to highlight the essence of the objects and discuss the theme of identity. The following geometric objects were constructed: any triangle and right triangle. The theoretical and philosophical foundation of the study was Edmund Husserl's Phenomenology, studied through the works of commentators such as Ales Bello, Sokolowski, and Bicudo. The method of data constitution and analysis followed a phenomenological approach, allowing for the application of eidetic reduction and imaginative variation. As a result of the research, it was found that the tools provided by the Geogebra software, such as fixed-length segment, line, slider, compass, and segment, played a fundamental role in constructing the geometric object, enabling it to continue representing the intended mathematical object even after the movement ceased. Furthermore, the phenomenological investigation unveiled the essence of the right triangle, which consists of having perpendicular lines as its legs. The essence of the any triangle object indicates that any side must have a length smaller than the sum of the other two sides. It was understood that the essences of the geometric objects found in the investigation converged with the definition or mathematical property of the respective objects. It was demonstrated that the right triangle belongs to the general category of triangles, and when it possesses the quality of being right-angled, it forms a new category dependent on the former. The identity of the any triangle object was shown to belong to the transcendental dimension and encompasses all types of triangles that can be drawn on paper and analyzed.