Propostas para o ensino de números complexos no ensino médio

Detalhes bibliográficos
Ano de defesa: 2014
Autor(a) principal: Silva, Fabiana Gerusa Leindeker da lattes
Orientador(a): Szinvelski, Charles Rogerio Paveglio lattes
Banca de defesa: Giuliani, Osmar Francisco, Magnago, Karine Faverzani
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal de Santa Maria
Centro de Ciências Naturais e Exatas
Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática em Rede Nacional
Departamento: Matemática
País: Brasil
Palavras-chave em Português:
Geometria
Números complexos
Forma polar
Rotações
Estratégias de ensino
Palavras-chave em Inglês:
Geometry
Complex number
Rotation
Polar form
Teaching strategies
Área do conhecimento CNPq:
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
Link de acesso: http://repositorio.ufsm.br/handle/1/21530
Resumo: This work explored the geometric properties of complex numbers. It presents a brief histor- ical contextualization, formalize the concepts, passing through the presentation of its algebraic form to its polar form and its geometric derivations. By means of this geometric bias is exam- ined in detail the operations of rotation, contraction and dilatation in the plane proportioned by the product of complex. As a consequence, we present an alternative proof of Napoleon’s Theo- rem, using immediately the product of complex numbers. Furthermore, are presented alternative proposals of work exploiting the interpretation of the analytic geometry problems experiencing efficient use of the properties of rotation resulting from the multiplication of complex num- bers. These proposals are directed to mathematics teachers in the 3rd year of high school with the goal of expanding the forms from presentation and treatment of complex numbers in their strategies for teaching this topic.
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spelling 2021-07-20T18:24:20Z2021-07-20T18:24:20Z2014-08-29http://repositorio.ufsm.br/handle/1/21530This work explored the geometric properties of complex numbers. It presents a brief histor- ical contextualization, formalize the concepts, passing through the presentation of its algebraic form to its polar form and its geometric derivations. By means of this geometric bias is exam- ined in detail the operations of rotation, contraction and dilatation in the plane proportioned by the product of complex. As a consequence, we present an alternative proof of Napoleon’s Theo- rem, using immediately the product of complex numbers. Furthermore, are presented alternative proposals of work exploiting the interpretation of the analytic geometry problems experiencing efficient use of the properties of rotation resulting from the multiplication of complex num- bers. These proposals are directed to mathematics teachers in the 3rd year of high school with the goal of expanding the forms from presentation and treatment of complex numbers in their strategies for teaching this topic.Não foi possível inserir o resumo.porUniversidade Federal de Santa MariaCentro de Ciências Naturais e ExatasPrograma de Pós-Graduação em Matemática em Rede NacionalUFSMBrasilMatemáticaAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessGeometriaNúmeros complexosForma polarRotaçõesEstratégias de ensinoGeometryComplex numberRotationPolar formTeaching strategiesCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAPropostas para o ensino de números complexos no ensino médioProposals for teaching complex numbers in secondary schoolinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisSzinvelski, Charles Rogerio Pavegliohttp://lattes.cnpq.br/2186097538587489Giuliani, Osmar FranciscoMagnago, Karine Faverzanihttp://lattes.cnpq.br/5654979708814595Silva, Fabiana Gerusa Leindeker da100100000008600600600ec093c27-7513-40d0-a63f-af8bd5e86d128f653d69-1835-4099-9b21-0a959e3c6d5e173b6107-3a6e-4f59-bca2-fb0f65779076078e6217-8731-47b5-8db2-8208d8052a60reponame:Manancial - Repositório Digital da UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.por.fl_str_mv Propostas para o ensino de números complexos no ensino médio
dc.title.alternative.eng.fl_str_mv Proposals for teaching complex numbers in secondary school
title Propostas para o ensino de números complexos no ensino médio
spellingShingle Propostas para o ensino de números complexos no ensino médio
Silva, Fabiana Gerusa Leindeker da
Geometria
Números complexos
Forma polar
Rotações
Estratégias de ensino
Geometry
Complex number
Rotation
Polar form
Teaching strategies
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Propostas para o ensino de números complexos no ensino médio
title_full Propostas para o ensino de números complexos no ensino médio
title_fullStr Propostas para o ensino de números complexos no ensino médio
title_full_unstemmed Propostas para o ensino de números complexos no ensino médio
title_sort Propostas para o ensino de números complexos no ensino médio
author Silva, Fabiana Gerusa Leindeker da
author_facet Silva, Fabiana Gerusa Leindeker da
author_role author
dc.contributor.advisor1.fl_str_mv Szinvelski, Charles Rogerio Paveglio
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/2186097538587489
dc.contributor.referee1.fl_str_mv Giuliani, Osmar Francisco
dc.contributor.referee2.fl_str_mv Magnago, Karine Faverzani
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/5654979708814595
dc.contributor.author.fl_str_mv Silva, Fabiana Gerusa Leindeker da
contributor_str_mv Szinvelski, Charles Rogerio Paveglio
Giuliani, Osmar Francisco
Magnago, Karine Faverzani
dc.subject.por.fl_str_mv Geometria
Números complexos
Forma polar
Rotações
Estratégias de ensino
topic Geometria
Números complexos
Forma polar
Rotações
Estratégias de ensino
Geometry
Complex number
Rotation
Polar form
Teaching strategies
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Geometry
Complex number
Rotation
Polar form
Teaching strategies
dc.subject.cnpq.fl_str_mv CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
description This work explored the geometric properties of complex numbers. It presents a brief histor- ical contextualization, formalize the concepts, passing through the presentation of its algebraic form to its polar form and its geometric derivations. By means of this geometric bias is exam- ined in detail the operations of rotation, contraction and dilatation in the plane proportioned by the product of complex. As a consequence, we present an alternative proof of Napoleon’s Theo- rem, using immediately the product of complex numbers. Furthermore, are presented alternative proposals of work exploiting the interpretation of the analytic geometry problems experiencing efficient use of the properties of rotation resulting from the multiplication of complex num- bers. These proposals are directed to mathematics teachers in the 3rd year of high school with the goal of expanding the forms from presentation and treatment of complex numbers in their strategies for teaching this topic.
publishDate 2014
dc.date.issued.fl_str_mv 2014-08-29
dc.date.accessioned.fl_str_mv 2021-07-20T18:24:20Z
dc.date.available.fl_str_mv 2021-07-20T18:24:20Z
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.uri.fl_str_mv http://repositorio.ufsm.br/handle/1/21530
url http://repositorio.ufsm.br/handle/1/21530
dc.language.iso.fl_str_mv por
language por
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dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Santa Maria
Centro de Ciências Naturais e Exatas
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática em Rede Nacional
dc.publisher.initials.fl_str_mv UFSM
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Matemática
publisher.none.fl_str_mv Universidade Federal de Santa Maria
Centro de Ciências Naturais e Exatas
dc.source.none.fl_str_mv reponame:Manancial - Repositório Digital da UFSM
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instname_str Universidade Federal de Santa Maria (UFSM)
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institution UFSM
reponame_str Manancial - Repositório Digital da UFSM
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