Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
dARK ID: | ark:/38995/00130000007nx |
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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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/6970ark:/38995/00130000007nxIn 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 |
format |
masterThesis |
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 |
dc.identifier.dark.fl_str_mv |
ark:/38995/00130000007nx |
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. ark:/38995/00130000007nx |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/6970 |
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por |
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por |
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4280721485626151024 |
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600 600 600 600 |
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-7090823417984401694 |
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2075167498588264571 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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Universidade Federal de Goiás |
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UFG |
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Brasil |
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Instituto de Matemática e Estatística - IME (RG) |
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Universidade Federal de Goiás |
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