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

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 resear...

ver descrição completa

Detalhes bibliográficos
Autor: Rêgo, Aderbal Soares do
Formato: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2022
País:Brasil
Recursos:Universidade Federal da Paraíba (UFPB)
Repositorio:Biblioteca Digital de Teses e Dissertações da UFPB
Idioma:portugués
OAI Identifier:oai:repositorio.ufpb.br:123456789/22827
Acesso em linha:https://repositorio.ufpb.br/jspui/handle/123456789/22827
Access Level:acceso abierto
Palavra-chave:Geometria plana
Áreas de polígonos
Malha quadriculada
Teorema de Pick
Plane geometry
Polygon areas
Checkered mesh
Pick’s Theorem
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
Descrição
Resumo: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.