Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra

Detalhes bibliográficos
Autor(a) principal: Carvalho, Wesley da Silva
Data de Publicação: 2016
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFG
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/6970
Resumo: In this dissertation, we first state Euler's polyhedral formula for a set of points with Euler characteristic 2. We address the two known ways to prove Euler's Theorem: beginning with the classical proof by using Euclidian Geometry and afterwards we take the advantage of Spherical Geometry to give another proof. Furthermore, we address a version of Euler's formula for planar polyhedron, as well as, Pick's formula and the equivalence between Euler and Pick's formula. In the end, we provide application of Euler and Pick's formula, via two pedagogy tools Geoplano and GeoGebra, by giving examples to teach in classroom.
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spelling Vieira, Ewerton Rochahttp://lattes.cnpq.br/9011778118531233Vieira, Ewerton RochaLourenço, Kélem GomesSouza, Flávio Raimundo dehttp://lattes.cnpq.br/6239424704355907Carvalho, Wesley da Silva2017-03-20T14:06:03Z2016-12-09CARVALHO, W. S. Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra. 2016. 52 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2016.http://repositorio.bc.ufg.br/tede/handle/tede/6970In this dissertation, we first state Euler's polyhedral formula for a set of points with Euler characteristic 2. We address the two known ways to prove Euler's Theorem: beginning with the classical proof by using Euclidian Geometry and afterwards we take the advantage of Spherical Geometry to give another proof. Furthermore, we address a version of Euler's formula for planar polyhedron, as well as, Pick's formula and the equivalence between Euler and Pick's formula. In the end, we provide application of Euler and Pick's formula, via two pedagogy tools Geoplano and GeoGebra, by giving examples to teach in classroom.Esta dissertação trata inicialmente da Fórmula de Euler e de sua validade para os conjuntos de pontos com característica de Euler igual a 2. São feitas duas demonstrações da Fórmula de Euler, uma utilizando conceitos de Geometria Euclidiana e uma outra via Geometria Esférica, além da apresentação de uma versão para poliedros planos da Fórmula de Euler. Posteriormente, é apresentada a Fórmula de Pick para o cálculo de áreas de polígonos simples reticulados e sua relação de equivalência com a Fórmula de Pick para poliedros planos. Finalmente mostramos duas possibilidades de trabalho com a Fórmula de Pick, no Geoplano e no software GeoGebra.Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2017-03-20T12:17:35Z No. of bitstreams: 2 Dissertação - Wesley da Silva Carvalho - 2016.pdf: 2739140 bytes, checksum: 009cb3705c3ac6a28927493419d88e0c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-03-20T14:06:03Z (GMT) No. of bitstreams: 2 Dissertação - Wesley da Silva Carvalho - 2016.pdf: 2739140 bytes, checksum: 009cb3705c3ac6a28927493419d88e0c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2017-03-20T14:06:03Z (GMT). No. of bitstreams: 2 Dissertação - Wesley da Silva Carvalho - 2016.pdf: 2739140 bytes, checksum: 009cb3705c3ac6a28927493419d88e0c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-12-09Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfporUniversidade Federal de GoiásPROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessFórmula de eulerFórmula de pickGeoplanoGeoGebraEuler's theoremPick's theoremGeoplanGeoGebraCIENCIAS EXATAS E DA TERRA::MATEMATICACálculo das fórmulas de Euler e Pick no geoplano e no GeoGebraEuler and pick’s numerical methods in calculus with geoplan and GeoGebrainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis4280721485626151024600600600600-4268777512335152015-70908234179844016942075167498588264571reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; 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dc.title.por.fl_str_mv Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra
dc.title.alternative.eng.fl_str_mv Euler and pick’s numerical methods in calculus with geoplan and GeoGebra
title Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra
spellingShingle Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra
Carvalho, Wesley da Silva
Fórmula de euler
Fórmula de pick
Geoplano
GeoGebra
Euler's theorem
Pick's theorem
Geoplan
GeoGebra
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra
title_full Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra
title_fullStr Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra
title_full_unstemmed Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra
title_sort Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra
author Carvalho, Wesley da Silva
author_facet Carvalho, Wesley da Silva
author_role author
dc.contributor.advisor1.fl_str_mv Vieira, Ewerton Rocha
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/9011778118531233
dc.contributor.referee1.fl_str_mv Vieira, Ewerton Rocha
dc.contributor.referee2.fl_str_mv Lourenço, Kélem Gomes
dc.contributor.referee3.fl_str_mv Souza, Flávio Raimundo de
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/6239424704355907
dc.contributor.author.fl_str_mv Carvalho, Wesley da Silva
contributor_str_mv Vieira, Ewerton Rocha
Vieira, Ewerton Rocha
Lourenço, Kélem Gomes
Souza, Flávio Raimundo de
dc.subject.por.fl_str_mv Fórmula de euler
Fórmula de pick
Geoplano
topic Fórmula de euler
Fórmula de pick
Geoplano
GeoGebra
Euler's theorem
Pick's theorem
Geoplan
GeoGebra
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv GeoGebra
Euler's theorem
Pick's theorem
Geoplan
GeoGebra
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description In this dissertation, we first state Euler's polyhedral formula for a set of points with Euler characteristic 2. We address the two known ways to prove Euler's Theorem: beginning with the classical proof by using Euclidian Geometry and afterwards we take the advantage of Spherical Geometry to give another proof. Furthermore, we address a version of Euler's formula for planar polyhedron, as well as, Pick's formula and the equivalence between Euler and Pick's formula. In the end, we provide application of Euler and Pick's formula, via two pedagogy tools Geoplano and GeoGebra, by giving examples to teach in classroom.
publishDate 2016
dc.date.issued.fl_str_mv 2016-12-09
dc.date.accessioned.fl_str_mv 2017-03-20T14:06:03Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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status_str publishedVersion
dc.identifier.citation.fl_str_mv CARVALHO, W. S. Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra. 2016. 52 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2016.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/6970
identifier_str_mv CARVALHO, W. S. Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra. 2016. 52 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2016.
url http://repositorio.bc.ufg.br/tede/handle/tede/6970
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language por
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dc.relation.confidence.fl_str_mv 600
600
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dc.publisher.initials.fl_str_mv UFG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Instituto de Matemática e Estatística - IME (RG)
publisher.none.fl_str_mv Universidade Federal de Goiás
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