Teorema de pick: apresentando uma forma de calcular áreas e a sua contribuição para o cálculo de volumes

Abstract

This work was built based on the Pick's Theorem and how to calculate areas in a differentiated way. The Pick's Theorem proves to be a powerful mathematical tool that allows the calculation of the area of simple polygons in a very effective way. Its approach is especially useful for polygons that are not regular, as it is not necessary to apply specific formulas for each type of polygon. In this work, you will also see in one of the chapters the contribution of this theorem in three-dimensional calculations, which it was extended to the calculation of volumes. In 2019, an application of the Pick's Theorem was conducted in a 9th-grade class at a Municipal School in Rio de Janeiro, where the students were able to experience a different way of working with polygons and, as a result, in addition to engaging in the learning process, they obtained very satisfactory results in the task application. The method proved to be efficient for the calculations performed, which highlights its importance as a tool for teaching and learning mathematics.