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Previous issue date: 2015-06-17 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work will concentrate on making a rereading of the theories that surround the
procedures for calculating the area of a convex polygon, as well as the volume of a
pyramid whose base is a polygon convex, with its vertices properly represented in a
coordinate system, in the plan or in space, respectively. Addresses some topics on arrays
and determinant and some of its applications, in particular the study of polygon area
and the volume of the pyramid. Based on applying a decisive factor for the calculation
of the area of a triangle with its vertices represented in a coordinate system, presents
a new theorem to calculate the area of any polygon convex, as well as, a new formula
to calculate the volume of any pyramid with convex basis as a direct application of the
volume of the tetrahedron with its vertices represented in an orthogonal system. For
both, it was essential to the concept of coordinates in the plane and in space, vectors in
the plane and in space, and some of its properties, being essential for the demonstrate
the volume of the tetrahedron and the area of the triangle, using determinant.
Keywords: Volume. Area. Convex polygon. Pyramid. Triangle. Tetrahedron / O presente trabalho versar a em fazer uma releitura das teorias que circundam os
procedimentos de c alculo da area de um pol gono convexo, assim como, do volume de
uma pir^amide cuja base e um pol gono convexo, com seus v ertices devidamente representados
em um sistema de coordenadas, no plano ou no espa co, respectivamente.
Aborda alguns t opicos sobre matrizes e determinante e algumas de suas aplica c~oes, em
especial o estudo de area de pol gonos e o volume de pir^amide. Baseado na aplica c~ao
de determinante para o c alculo da area de um tri^angulo com seus v ertices representados
em um sistema de coordenadas, apresenta um novo teorema para o c alculo da
area de qualquer pol gono convexo, assim como, uma nova f ormula para calcular o volume
de qualquer pir^amide com base convexa como uma aplica c~ao direta do volume do
tetraedro com seus v ertices representados em um sistema ortogonal. Para tanto, foi imprescind
vel abordar o conceito de coordenadas no plano e no espa co, vetores no plano
e no espa co e algumas de suas propriedades, sendo fundamentais para a demonstrar o
volume do tetraedro e a area do tri^angulo, usando determinante.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.bc.ufg.br:tede/4728 |
| Date | 17 June 2015 |
| Creators | Araujo, Elismar Jose de |
| Contributors | Freitas, Thiago Porto de Almeida, Freitas, Thiago Porto de Almeida, Leandro, Bianka Carneiro, Oliveira, Plínio José |
| Publisher | Universidade Federal de Goiás, Programa de Pós-graduação em PROFMAT (RC), UFG, Brasil, Regional de Catalão (RC) |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| Source | reponame:Biblioteca Digital de Teses e Dissertações da UFG, instname:Universidade Federal de Goiás, instacron:UFG |
| Rights | http://creativecommons.org/licenses/by-nc-nd/4.0/, info:eu-repo/semantics/openAccess |
| Relation | -1366297389077119106, 600, 600, 600, 600, -6789486854152681716, -7090823417984401694, 2075167498588264571 |
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