Discussões sobre o cálculo de áreas: uma proposta heurística para o ensino-aprendizagem

Abstract

This work seeks to present strategies for the construction of knowledge about the calculation of polygonal and non-polygonal areas through the exploration of basic concepts of areas of flat figures in a simple and direct way, enabling students and teachers to understand and use this material to study or preparation of classes. At first, tehniques used in the history of mathematics to calculate polygonal areas and the Eudoxo Exhaustion Method, used to find the area of the area of the circle, are presented. Then, an approach is made that consists of partitioning a polygonal region into finite triangular regions using different techniques for their calculation, suh as triangulation and Heron’s formula. The aim is to expand the calculation of areas to irregular polygonal regions, through Pick’s Formula, associating them with the mapping and calculation of territorial extensions. Finally, the concept of integral and its application in the calculation of areas is discussed, and a summarized approach is made to Green’s Theorem, its relationship with the planimeter and its application to te calculation of areas.