Evolução do cálculo de áreas de figuras planas: do ensino básico ao ensino superior.

Abstract

This work is characterized as an exploratory bibliographical research, where we present the evolution of the calculation of areas of flat figures from elementary school to higher education. The problem of calculating areas has been of interest to mankind since antiquity when it was sought to measure and demarcate lands up to the present day in several areas such as Civil Engineering, Architecture and Urbanism, for example, and this was what motivated our study. In primary and secondary education, one already has the notion of determining the area of some flat figures and for this, mathematical formulas are used. However, when it comes to a figure with curved contours, such as the one delimited by functions, there is no predefined formula and more sophisticated mathematical tools are needed such as the Fundamental Theorem of Calculus, Fubinni’s Theorem or Green’s Theorem. The text, in which we present our research, begins with a brief history about geometry and integral calculus, then we use flat geometry to explain, with some mathematical rigor, the demonstration of some formulas seen in elementary education. And through integral calculus and its tools we deal with areas of figures with curved contours, which are studied in higher education. The present research allowed us to observe that there are several studies focused on the calculation of areas, however it is not very common to bring this approach from basic to higher education