O equilíbrio dos planos e os pontos notáveis do triângulo: Arquimedes, Euclides e origami trabalhando juntos
Autor(a) principal: | |
---|---|
Data de Publicação: | 2021 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional Manancial UFSM |
Texto Completo: | http://repositorio.ufsm.br/handle/1/21168 |
Resumo: | This paper aims to explore a new way to study geometry during the High School, using physics and origami. We use classical works of Archimedes and Euclid to rise the mathemathical way to study the properties of the plane figures’ center of mass and the triangle’s notable points. Walking on the knowledge timeline we add some contributions made by the french mathematician Hadamard and modern ways to teaching geometry at school. In fact, we try to compare old and modern classroom practices. Them, we present some aspects about the origin of origami in Japan and paperfolding in western contries. After, we talk about Huzita-Hatori Axioms in mathematical terms. In order to use the natural young people curiosity about things we show the physical center of mass concept and argue about the geometry usefulness in the real world. Finally, we present how its possible to work in two diferente ways to find the plane figures’ center of mass and the triangle’s notable points: the classical way, using a straight edge and a compass for the mathematical constructions and the funny way, using origami to do the same. All of these will be done looking foward teachers and students realize that’s possible to have good time while they are studing Mathematics. We also hope this work may inspire teachers to encourage their students to share mathematical knowlegmente outside the school. |
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2021-06-21T20:17:35Z2021-06-21T20:17:35Z2021-01-28http://repositorio.ufsm.br/handle/1/21168This paper aims to explore a new way to study geometry during the High School, using physics and origami. We use classical works of Archimedes and Euclid to rise the mathemathical way to study the properties of the plane figures’ center of mass and the triangle’s notable points. Walking on the knowledge timeline we add some contributions made by the french mathematician Hadamard and modern ways to teaching geometry at school. In fact, we try to compare old and modern classroom practices. Them, we present some aspects about the origin of origami in Japan and paperfolding in western contries. After, we talk about Huzita-Hatori Axioms in mathematical terms. In order to use the natural young people curiosity about things we show the physical center of mass concept and argue about the geometry usefulness in the real world. Finally, we present how its possible to work in two diferente ways to find the plane figures’ center of mass and the triangle’s notable points: the classical way, using a straight edge and a compass for the mathematical constructions and the funny way, using origami to do the same. All of these will be done looking foward teachers and students realize that’s possible to have good time while they are studing Mathematics. We also hope this work may inspire teachers to encourage their students to share mathematical knowlegmente outside the school.Este trabalho pretende explorar uma nova maneira de estudar geometria no Ensino Médio, usando a física e os origamis. Nesse mister, recorre-se aos ensinamentos dos mestres clássicos Arquimedes e Euclides para estabelecer o ponto de partida do pensamento matemático relacionado ao estudo dos Centros de Gravidade das Figuras Planas e dos Pontos Notáveis do Triângulo. Caminhando sobre a linha do tempo do conhecimento somam-se as contribuições do matemático francês Hadamard e as práticas atuais do ensino da geometria em sala de aula, tentando fazer uma breve comparação entre as técnicas clássicas e as modernas. Preparando a atividade interdisciplinar, faz-se um rápido estudo das origens das dobraduras em papel, chamadas origami no Japão e papiroflexia no ocidente. Posteriormente, os Axiomas de Huzita- Hatori são apresentados em termos matemáticos. O conceito físico de Centro de Gravidade é adicionado para servir de catalizador da curiosidade dos estudantes para encararem a geometria como uma ciência que está presente no seu cotidiano. Finalmente, o estudo dos Centros de Gravidade dos Planos e dos Pontos Notáveis do Triângulo é apresentado de duas maneiras diferentes: uma clássica usando régua e compasso para as construções matemáticas e outra lúdica, com uso dos origamis, para fazer o mesmo. Espera-se que professores e alunos percebam que podem se divertir enquanto estudam Matemática. Além disso, espera-se que este trabalho inspire os professores a estimularem os seus alunos a compartilhar o seu conhecimento matemático fora do ambiente de sala de aula.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/openAccessCentro de gravidadePontos notáveis do triânguloPapiroflexiaOrigami na matemáticaEnsino de geometria planaMatemática dos axiomas de Huzita-HatoriCenter of massTriangle’s notable pointsPaper foldingMathematical origamiTeaching plane geometryHuzita-Hatori axioms on mathematical wordsCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAO equilíbrio dos planos e os pontos notáveis do triângulo: Arquimedes, Euclides e origami trabalhando juntosOn the equilibrium of planes and the triangle’s notable points: Archimedes, Euclid, Huzita and Hatori working togetherinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisFigueiredo, Edson Sidneyhttp://lattes.cnpq.br/1112919781647346Pansonato, Cláudia CandidaSauer, Lisandra de Oliveirahttp://lattes.cnpq.br/8806831416326222Pereira, Luiz Fernando10010000000860007cc44c6-bbcf-4946-82b0-f87e4536387b347ffcc3-c912-404e-bb68-d073458640d5af96a68c-3d0f-4883-87d6-e725b93296ec10b4ddcf-2890-4707-9e72-69813c8fbd48reponame:Repositório Institucional Manancial UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMLICENSElicense.txtlicense.txttext/plain; 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dc.title.por.fl_str_mv |
O equilíbrio dos planos e os pontos notáveis do triângulo: Arquimedes, Euclides e origami trabalhando juntos |
dc.title.alternative.eng.fl_str_mv |
On the equilibrium of planes and the triangle’s notable points: Archimedes, Euclid, Huzita and Hatori working together |
title |
O equilíbrio dos planos e os pontos notáveis do triângulo: Arquimedes, Euclides e origami trabalhando juntos |
spellingShingle |
O equilíbrio dos planos e os pontos notáveis do triângulo: Arquimedes, Euclides e origami trabalhando juntos Pereira, Luiz Fernando Centro de gravidade Pontos notáveis do triângulo Papiroflexia Origami na matemática Ensino de geometria plana Matemática dos axiomas de Huzita-Hatori Center of mass Triangle’s notable points Paper folding Mathematical origami Teaching plane geometry Huzita-Hatori axioms on mathematical words CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
O equilíbrio dos planos e os pontos notáveis do triângulo: Arquimedes, Euclides e origami trabalhando juntos |
title_full |
O equilíbrio dos planos e os pontos notáveis do triângulo: Arquimedes, Euclides e origami trabalhando juntos |
title_fullStr |
O equilíbrio dos planos e os pontos notáveis do triângulo: Arquimedes, Euclides e origami trabalhando juntos |
title_full_unstemmed |
O equilíbrio dos planos e os pontos notáveis do triângulo: Arquimedes, Euclides e origami trabalhando juntos |
title_sort |
O equilíbrio dos planos e os pontos notáveis do triângulo: Arquimedes, Euclides e origami trabalhando juntos |
author |
Pereira, Luiz Fernando |
author_facet |
Pereira, Luiz Fernando |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Figueiredo, Edson Sidney |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/1112919781647346 |
dc.contributor.referee1.fl_str_mv |
Pansonato, Cláudia Candida |
dc.contributor.referee2.fl_str_mv |
Sauer, Lisandra de Oliveira |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/8806831416326222 |
dc.contributor.author.fl_str_mv |
Pereira, Luiz Fernando |
contributor_str_mv |
Figueiredo, Edson Sidney Pansonato, Cláudia Candida Sauer, Lisandra de Oliveira |
dc.subject.por.fl_str_mv |
Centro de gravidade Pontos notáveis do triângulo Papiroflexia Origami na matemática Ensino de geometria plana Matemática dos axiomas de Huzita-Hatori |
topic |
Centro de gravidade Pontos notáveis do triângulo Papiroflexia Origami na matemática Ensino de geometria plana Matemática dos axiomas de Huzita-Hatori Center of mass Triangle’s notable points Paper folding Mathematical origami Teaching plane geometry Huzita-Hatori axioms on mathematical words CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Center of mass Triangle’s notable points Paper folding Mathematical origami Teaching plane geometry Huzita-Hatori axioms on mathematical words |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This paper aims to explore a new way to study geometry during the High School, using physics and origami. We use classical works of Archimedes and Euclid to rise the mathemathical way to study the properties of the plane figures’ center of mass and the triangle’s notable points. Walking on the knowledge timeline we add some contributions made by the french mathematician Hadamard and modern ways to teaching geometry at school. In fact, we try to compare old and modern classroom practices. Them, we present some aspects about the origin of origami in Japan and paperfolding in western contries. After, we talk about Huzita-Hatori Axioms in mathematical terms. In order to use the natural young people curiosity about things we show the physical center of mass concept and argue about the geometry usefulness in the real world. Finally, we present how its possible to work in two diferente ways to find the plane figures’ center of mass and the triangle’s notable points: the classical way, using a straight edge and a compass for the mathematical constructions and the funny way, using origami to do the same. All of these will be done looking foward teachers and students realize that’s possible to have good time while they are studing Mathematics. We also hope this work may inspire teachers to encourage their students to share mathematical knowlegmente outside the school. |
publishDate |
2021 |
dc.date.accessioned.fl_str_mv |
2021-06-21T20:17:35Z |
dc.date.available.fl_str_mv |
2021-06-21T20:17:35Z |
dc.date.issued.fl_str_mv |
2021-01-28 |
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.uri.fl_str_mv |
http://repositorio.ufsm.br/handle/1/21168 |
url |
http://repositorio.ufsm.br/handle/1/21168 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.cnpq.fl_str_mv |
100100000008 |
dc.relation.confidence.fl_str_mv |
600 |
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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 |
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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:Repositório Institucional Manancial UFSM instname:Universidade Federal de Santa Maria (UFSM) instacron:UFSM |
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