O Teorema de Pick no ensino-aprendizagem da geometria plana: cálculo de áreas de polígonos simples

Abstract

This dissertation aims to present an alternative proposal for the teaching of the area of the simple polygoms, overlaied in a checkered mesh wich the vertices are integer coordinates, that are present in various contexts in the Basic Education, using the Pick’s theorem. Based on bibliographic research, initially, will be studied a few basic concepts of plain geometry that will give support to a demonstrative apresentation of the Pick’s Theorem. Following it a small historic apresentation about the matematician George Alexander Pick, the development of his theorem and a demonstration in two different ways of its use.Next, the demonstration of this theorem in the physical geoplane and on-line, its version to the polygonoms with holes and a estimative of the value of π. Following, we present some questions, with its respective solutions, extracted from matematical national exams that stimulated students by the subject, making the classes more interesting.