Cônicas e suas propriedades refletoras
Autor(a) principal: | |
---|---|
Data de Publicação: | 2018 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Manancial - Repositório Digital da UFSM |
Texto Completo: | http://repositorio.ufsm.br/handle/1/16261 |
Resumo: | The objective of this work is to present and demonstrate the reflective properties of the conics, as well as to understand why these geometric figures have fascinated mathematicians since antiquity. Mathematical demonstrations were prioritized with the help of Geometry and Algebra. The use of differential and integral calculus resources was avoided, since this work is aimed at the students of the Middle School, who do not have knowledge of these mathematical resources. In a first moment we analyzed the reasons why these geometric figures receive so little attention in the curriculum of Middle School. It was opportune to analyze a small collection of books recommended by the Ministry of Education (MEC), listed in National Textbook Program (PNLD). It is possible to perceive a very superficial approach to conics, especially hyperbole and ellipse, although the parable in some books is studied in more depth, normaly representing the graphic of a quadratic function. Next we present a brief exposition on the historical origins of the conics, where we highlight the four main protagonists of the theme: Pythagoras, Euclid, Archimedes and Apollonius. We study, separately, each conic from its definition, followed by an algebraic development to find the equation that defines it. We emphasize their reflective properties and how to use them in the creation of technological equipment that helps in the scientific evolution of man. Following are examples of equipment that use technology using the principles of conics. The software Geogebra, Paint.net, Google Sketchup 8.0 and Gimp 2.0, were used as computational tools to elaborate the figures in this work. |
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2019-04-18T14:27:14Z2019-04-18T14:27:14Z2018-08-20http://repositorio.ufsm.br/handle/1/16261The objective of this work is to present and demonstrate the reflective properties of the conics, as well as to understand why these geometric figures have fascinated mathematicians since antiquity. Mathematical demonstrations were prioritized with the help of Geometry and Algebra. The use of differential and integral calculus resources was avoided, since this work is aimed at the students of the Middle School, who do not have knowledge of these mathematical resources. In a first moment we analyzed the reasons why these geometric figures receive so little attention in the curriculum of Middle School. It was opportune to analyze a small collection of books recommended by the Ministry of Education (MEC), listed in National Textbook Program (PNLD). It is possible to perceive a very superficial approach to conics, especially hyperbole and ellipse, although the parable in some books is studied in more depth, normaly representing the graphic of a quadratic function. Next we present a brief exposition on the historical origins of the conics, where we highlight the four main protagonists of the theme: Pythagoras, Euclid, Archimedes and Apollonius. We study, separately, each conic from its definition, followed by an algebraic development to find the equation that defines it. We emphasize their reflective properties and how to use them in the creation of technological equipment that helps in the scientific evolution of man. Following are examples of equipment that use technology using the principles of conics. The software Geogebra, Paint.net, Google Sketchup 8.0 and Gimp 2.0, were used as computational tools to elaborate the figures in this work.O objetivo deste trabalho é apresentar e demonstrar as propriedades refletoras das cônicas, bem como entender o porquê destas figuras geométricas fascinarem os matemáticos desde a antiguidade. Foram priorizadas as demonstrações matemáticas com o auxílio da Geometria e Álgebra. Evitou-se a utilização de recursos do cálculo diferencial e integral, haja vista que este trabalho é voltado aos alunos do ensino Médio, os quais não possuem conhecimento desses recursos matemáticos. Em um primeiro momento analisamos os motivos de estas figuras geométricas receberem tão pouca atenção no currículo do ensino Médio. Foi oportuno analisarmos uma pequena coletânea de livros recomendados pelo Ministério da Educação (MEC), constantes no Programa Nacional do Livro Didático (PNLD). É possível perceber uma abordagem muito superficial em relação às cônicas, especialmente a hipérbole e a elipse, embora a parábola, em alguns livros, seja estudada com mais profundidade, normalmente representando o gráfico de uma função quadrática. Em seguida, apresentamos uma breve exposição sobre as origens históricas das cônicas, onde destacamos os quatro principais protagonistas do tema: Pitágoras, Euclides, Arquimedes e Apolônio. Estudamos, separadamente, cada cônica a partir de sua definição, seguido de um desenvolvimento algébrico para encontrarmos a equação que a define. Ressaltamos suas propriedades refletoras e como usá-las na criação de equipamentos tecnológicos que ajudem na evolução científica do homem. Dando continuidade apresentamos exemplos de equipamentos que usam tecnologia utilizando os princípios das cônicas. Os softwares Geogebra, Paint.net, Google Sketcup 8.0 e Gimp 2.0, foram utilizados como ferramentas computacionais para a elaboração das figuras neste trabalho.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/openAccessPropriedade das cônicasElipseHipérboleParábolaHistória da matemáticaEnsino médioCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICACônicas e suas propriedades refletorasConical and its reflective propertiesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisGomes, Denilsonhttp://lattes.cnpq.br/8116912195059700Buligon, Lidianehttp://lattes.cnpq.br/4755671184790141Oliveira, Vinicius de Abreuhttp://lattes.cnpq.br/2010283569069232http://lattes.cnpq.br/6840745342448869Barbieri, Claudir Dias10010000000860090915dd2-1c58-4923-82b3-15a224d55e56461c6176-f62d-4438-a87e-c7e2b967fc1582092a0c-0f5c-471a-b38b-5595bd5bd39b33431f5e-64c0-44e2-b245-10d35db7280creponame: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 |
Cônicas e suas propriedades refletoras |
dc.title.alternative.eng.fl_str_mv |
Conical and its reflective properties |
title |
Cônicas e suas propriedades refletoras |
spellingShingle |
Cônicas e suas propriedades refletoras Barbieri, Claudir Dias Propriedade das cônicas Elipse Hipérbole Parábola História da matemática Ensino médio CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Cônicas e suas propriedades refletoras |
title_full |
Cônicas e suas propriedades refletoras |
title_fullStr |
Cônicas e suas propriedades refletoras |
title_full_unstemmed |
Cônicas e suas propriedades refletoras |
title_sort |
Cônicas e suas propriedades refletoras |
author |
Barbieri, Claudir Dias |
author_facet |
Barbieri, Claudir Dias |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Gomes, Denilson |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8116912195059700 |
dc.contributor.referee1.fl_str_mv |
Buligon, Lidiane |
dc.contributor.referee1Lattes.fl_str_mv |
http://lattes.cnpq.br/4755671184790141 |
dc.contributor.referee2.fl_str_mv |
Oliveira, Vinicius de Abreu |
dc.contributor.referee2Lattes.fl_str_mv |
http://lattes.cnpq.br/2010283569069232 |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/6840745342448869 |
dc.contributor.author.fl_str_mv |
Barbieri, Claudir Dias |
contributor_str_mv |
Gomes, Denilson Buligon, Lidiane Oliveira, Vinicius de Abreu |
dc.subject.por.fl_str_mv |
Propriedade das cônicas Elipse Hipérbole Parábola História da matemática Ensino médio |
topic |
Propriedade das cônicas Elipse Hipérbole Parábola História da matemática Ensino médio CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
The objective of this work is to present and demonstrate the reflective properties of the conics, as well as to understand why these geometric figures have fascinated mathematicians since antiquity. Mathematical demonstrations were prioritized with the help of Geometry and Algebra. The use of differential and integral calculus resources was avoided, since this work is aimed at the students of the Middle School, who do not have knowledge of these mathematical resources. In a first moment we analyzed the reasons why these geometric figures receive so little attention in the curriculum of Middle School. It was opportune to analyze a small collection of books recommended by the Ministry of Education (MEC), listed in National Textbook Program (PNLD). It is possible to perceive a very superficial approach to conics, especially hyperbole and ellipse, although the parable in some books is studied in more depth, normaly representing the graphic of a quadratic function. Next we present a brief exposition on the historical origins of the conics, where we highlight the four main protagonists of the theme: Pythagoras, Euclid, Archimedes and Apollonius. We study, separately, each conic from its definition, followed by an algebraic development to find the equation that defines it. We emphasize their reflective properties and how to use them in the creation of technological equipment that helps in the scientific evolution of man. Following are examples of equipment that use technology using the principles of conics. The software Geogebra, Paint.net, Google Sketchup 8.0 and Gimp 2.0, were used as computational tools to elaborate the figures in this work. |
publishDate |
2018 |
dc.date.issued.fl_str_mv |
2018-08-20 |
dc.date.accessioned.fl_str_mv |
2019-04-18T14:27:14Z |
dc.date.available.fl_str_mv |
2019-04-18T14:27:14Z |
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/1/16261 |
url |
http://repositorio.ufsm.br/handle/1/16261 |
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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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/ |
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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 |
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