Elipse de Steiner

Detalhes bibliográficos
Autor(a) principal: Santana, Gleisson Rodrigues
Data de Publicação: 2014
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFG
dARK ID: ark:/38995/00130000087nb
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/4184
Resumo: This work is focused on demonstrating, using geometric tools, the Steiner's Ellipse theorem which says that all ellipses entered in a given triangle, the larger area is touching the triangle sides in their respective middle points. For this we did, in chapter one, an approach to the study of triangles, the ellipses, the orthogonal projection, and we present some results of arithmetic and geometry, this work titled as preliminary lemmas, to be the tools (prerequisites) for proof the theorem that the main is made in chapter two. We conclude by presenting, in chapter three, some applications and some scripts for lessons in how to use the ellipse, and in particular Steiner's Ellipse, day-to-day and in the classroom.
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spelling Rodrigues, Paulo Henrique de Azevedohttp://lattes.cnpq.br/8910130626123426Rodrigues, Paulo Henrique de AzevedoSilva, Sílvia Cristina Belo eSantos, Fabiano Fortunato Teixeira doshttp://lattes.cnpq.br/7697589143054464Santana, Gleisson Rodrigues2015-02-20T11:23:23Z2014-09-26SANTANA, G. R. Elipse de Steiner. 2014. 77 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional)–Universidade Federal de Goiás, Goiânia, 2014.http://repositorio.bc.ufg.br/tede/handle/tede/4184ark:/38995/00130000087nbThis work is focused on demonstrating, using geometric tools, the Steiner's Ellipse theorem which says that all ellipses entered in a given triangle, the larger area is touching the triangle sides in their respective middle points. For this we did, in chapter one, an approach to the study of triangles, the ellipses, the orthogonal projection, and we present some results of arithmetic and geometry, this work titled as preliminary lemmas, to be the tools (prerequisites) for proof the theorem that the main is made in chapter two. We conclude by presenting, in chapter three, some applications and some scripts for lessons in how to use the ellipse, and in particular Steiner's Ellipse, day-to-day and in the classroom.Este trabalho tem como tema central demonstrar, usando ferramentas geométricas, o teorema da Elipse de Steiner que diz que de todas as elipses inscritas em um triângulo dado, a de maior área é a que toca os lados do triângulo nos seus respectivos pontos médios. Para isto zemos, no Capítulo um, uma abordagem sobre o estudo dos triângulos, da elispse, e da projeção ortogonal, e apresentamos alguns resultados de aritmética e geometria, neste trabalho intitulados como lemas preliminares, para serem as ferramentas (os pré-requisitos) para a demonstração do teorema principal, que é feita no Capítulo dois. Concluímos o trabalho apresentando, no Capítulo três, algumas aplicações e alguns roteiros de aulas, de como utilizar a elipse, e em particular a Elipse de Steiner, no dia-a-dia e na sala de aula.Submitted by Luanna Matias (lua_matias@yahoo.com.br) on 2015-02-09T14:23:51Z No. of bitstreams: 2 Dissertação - Gleisson Rodrigues Santana - 2014.pdf: 8324640 bytes, checksum: 7800065ef09bc6ed1b331e277537350b (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-02-20T11:23:23Z (GMT) No. of bitstreams: 2 Dissertação - Gleisson Rodrigues Santana - 2014.pdf: 8324640 bytes, checksum: 7800065ef09bc6ed1b331e277537350b (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Made available in DSpace on 2015-02-20T11:23:23Z (GMT). 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dc.title.eng.fl_str_mv Elipse de Steiner
dc.title.alternative.eng.fl_str_mv Steiner's Ellipse
title Elipse de Steiner
spellingShingle Elipse de Steiner
Santana, Gleisson Rodrigues
Elipse de Steiner
Elipses e suas propriedades
Aplicações da Elipse
Roteiros de aula sobre Elipse
Steiner's Ellipse
Ellipses and their properties
Applications of Ellipse
Journeys lesson about Ellipse
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Elipse de Steiner
title_full Elipse de Steiner
title_fullStr Elipse de Steiner
title_full_unstemmed Elipse de Steiner
title_sort Elipse de Steiner
author Santana, Gleisson Rodrigues
author_facet Santana, Gleisson Rodrigues
author_role author
dc.contributor.advisor1.fl_str_mv Rodrigues, Paulo Henrique de Azevedo
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/8910130626123426
dc.contributor.referee1.fl_str_mv Rodrigues, Paulo Henrique de Azevedo
dc.contributor.referee2.fl_str_mv Silva, Sílvia Cristina Belo e
dc.contributor.referee3.fl_str_mv Santos, Fabiano Fortunato Teixeira dos
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/7697589143054464
dc.contributor.author.fl_str_mv Santana, Gleisson Rodrigues
contributor_str_mv Rodrigues, Paulo Henrique de Azevedo
Rodrigues, Paulo Henrique de Azevedo
Silva, Sílvia Cristina Belo e
Santos, Fabiano Fortunato Teixeira dos
dc.subject.por.fl_str_mv Elipse de Steiner
Elipses e suas propriedades
Aplicações da Elipse
Roteiros de aula sobre Elipse
topic Elipse de Steiner
Elipses e suas propriedades
Aplicações da Elipse
Roteiros de aula sobre Elipse
Steiner's Ellipse
Ellipses and their properties
Applications of Ellipse
Journeys lesson about Ellipse
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Steiner's Ellipse
Ellipses and their properties
Applications of Ellipse
Journeys lesson about Ellipse
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description This work is focused on demonstrating, using geometric tools, the Steiner's Ellipse theorem which says that all ellipses entered in a given triangle, the larger area is touching the triangle sides in their respective middle points. For this we did, in chapter one, an approach to the study of triangles, the ellipses, the orthogonal projection, and we present some results of arithmetic and geometry, this work titled as preliminary lemmas, to be the tools (prerequisites) for proof the theorem that the main is made in chapter two. We conclude by presenting, in chapter three, some applications and some scripts for lessons in how to use the ellipse, and in particular Steiner's Ellipse, day-to-day and in the classroom.
publishDate 2014
dc.date.issued.fl_str_mv 2014-09-26
dc.date.accessioned.fl_str_mv 2015-02-20T11:23:23Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
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dc.identifier.citation.fl_str_mv SANTANA, G. R. Elipse de Steiner. 2014. 77 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional)–Universidade Federal de Goiás, Goiânia, 2014.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/4184
dc.identifier.dark.fl_str_mv ark:/38995/00130000087nb
identifier_str_mv SANTANA, G. R. Elipse de Steiner. 2014. 77 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional)–Universidade Federal de Goiás, Goiânia, 2014.
ark:/38995/00130000087nb
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dc.publisher.none.fl_str_mv Universidade Federal de Goiás
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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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