Solução dos três problemas clássicos da matemática grega por curvas mecânicas
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Manancial - Repositório Digital da UFSM |
Texto Completo: | http://repositorio.ufsm.br/handle/1/21532 |
Resumo: | This study aims at displaying the beginning of the development of Mathematics, within a geometrical perspective, covering the methods of resolution, known today as the three classical problems of the Greek Mathematics: squaring the circle, trisecting the angle and doubling the cube. Besides that, this dissertation talks about the work of some great mathematicians of the ancient times, who are Archimedes, Dinostrato, Eratosthenes, Hippias, Pappus and Nicomedes. These mathematicians leaned over the referred problems and o ered very elegant solutions, by means of the use of mechanical curves, such as the quadratrix or trisectrix, the conchoids and the cissoids, although the desired ones, initially, were the so called Euclidean constructions, that is, the constructions done only with ruler and a compass. In this work, it is also presented the neusis constructions, responsible for a signi cant part of the trisection solutions. This work can help others who are interested in the matter, once it shows the importance of geometry for the fostering of the development of all Mathematical knowledge. |
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Solução dos três problemas clássicos da matemática grega por curvas mecânicasSolution of the three classical problems of the greek mathematics with mechanical curvesGeometriaProblemas cl ássicosQuadratura do c írculoTrissecção do ânguloDuplicação do cuboGeometryClassical problemsSquaring the circleTrisection angleDoubling the cubeCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAThis study aims at displaying the beginning of the development of Mathematics, within a geometrical perspective, covering the methods of resolution, known today as the three classical problems of the Greek Mathematics: squaring the circle, trisecting the angle and doubling the cube. Besides that, this dissertation talks about the work of some great mathematicians of the ancient times, who are Archimedes, Dinostrato, Eratosthenes, Hippias, Pappus and Nicomedes. These mathematicians leaned over the referred problems and o ered very elegant solutions, by means of the use of mechanical curves, such as the quadratrix or trisectrix, the conchoids and the cissoids, although the desired ones, initially, were the so called Euclidean constructions, that is, the constructions done only with ruler and a compass. In this work, it is also presented the neusis constructions, responsible for a signi cant part of the trisection solutions. This work can help others who are interested in the matter, once it shows the importance of geometry for the fostering of the development of all Mathematical knowledge.Não foi possível inserir o resumo.Universidade Federal de Santa MariaBrasilMatemáticaUFSMPrograma de Pós-Graduação em Matemática em Rede NacionalCentro de Ciências Naturais e ExatasFigueiredo, Edson Sidneyhttp://lattes.cnpq.br/1112919781647346Gomes, DenilsonBinotto, Rosane RossatoD'Acampora, Raphael2021-07-20T19:05:01Z2021-07-20T19:05:01Z2014-08-29info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttp://repositorio.ufsm.br/handle/1/21532porAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessreponame:Manancial - Repositório Digital da UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSM2021-07-21T06:02:12Zoai:repositorio.ufsm.br:1/21532Biblioteca Digital de Teses e Dissertaçõeshttps://repositorio.ufsm.br/ONGhttps://repositorio.ufsm.br/oai/requestatendimento.sib@ufsm.br||tedebc@gmail.comopendoar:2021-07-21T06:02:12Manancial - Repositório Digital da UFSM - Universidade Federal de Santa Maria (UFSM)false |
dc.title.none.fl_str_mv |
Solução dos três problemas clássicos da matemática grega por curvas mecânicas Solution of the three classical problems of the greek mathematics with mechanical curves |
title |
Solução dos três problemas clássicos da matemática grega por curvas mecânicas |
spellingShingle |
Solução dos três problemas clássicos da matemática grega por curvas mecânicas D'Acampora, Raphael Geometria Problemas cl ássicos Quadratura do c írculo Trissecção do ângulo Duplicação do cubo Geometry Classical problems Squaring the circle Trisection angle Doubling the cube CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Solução dos três problemas clássicos da matemática grega por curvas mecânicas |
title_full |
Solução dos três problemas clássicos da matemática grega por curvas mecânicas |
title_fullStr |
Solução dos três problemas clássicos da matemática grega por curvas mecânicas |
title_full_unstemmed |
Solução dos três problemas clássicos da matemática grega por curvas mecânicas |
title_sort |
Solução dos três problemas clássicos da matemática grega por curvas mecânicas |
author |
D'Acampora, Raphael |
author_facet |
D'Acampora, Raphael |
author_role |
author |
dc.contributor.none.fl_str_mv |
Figueiredo, Edson Sidney http://lattes.cnpq.br/1112919781647346 Gomes, Denilson Binotto, Rosane Rossato |
dc.contributor.author.fl_str_mv |
D'Acampora, Raphael |
dc.subject.por.fl_str_mv |
Geometria Problemas cl ássicos Quadratura do c írculo Trissecção do ângulo Duplicação do cubo Geometry Classical problems Squaring the circle Trisection angle Doubling the cube CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
topic |
Geometria Problemas cl ássicos Quadratura do c írculo Trissecção do ângulo Duplicação do cubo Geometry Classical problems Squaring the circle Trisection angle Doubling the cube CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This study aims at displaying the beginning of the development of Mathematics, within a geometrical perspective, covering the methods of resolution, known today as the three classical problems of the Greek Mathematics: squaring the circle, trisecting the angle and doubling the cube. Besides that, this dissertation talks about the work of some great mathematicians of the ancient times, who are Archimedes, Dinostrato, Eratosthenes, Hippias, Pappus and Nicomedes. These mathematicians leaned over the referred problems and o ered very elegant solutions, by means of the use of mechanical curves, such as the quadratrix or trisectrix, the conchoids and the cissoids, although the desired ones, initially, were the so called Euclidean constructions, that is, the constructions done only with ruler and a compass. In this work, it is also presented the neusis constructions, responsible for a signi cant part of the trisection solutions. This work can help others who are interested in the matter, once it shows the importance of geometry for the fostering of the development of all Mathematical knowledge. |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014-08-29 2021-07-20T19:05:01Z 2021-07-20T19:05:01Z |
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/1/21532 |
url |
http://repositorio.ufsm.br/handle/1/21532 |
dc.language.iso.fl_str_mv |
por |
language |
por |
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.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Brasil Matemática UFSM Programa de Pós-Graduação em Matemática em Rede Nacional Centro de Ciências Naturais e Exatas |
publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Brasil Matemática UFSM Programa de Pós-Graduação em Matemática em Rede Nacional Centro de Ciências Naturais e Exatas |
dc.source.none.fl_str_mv |
reponame:Manancial - Repositório Digital da UFSM instname:Universidade Federal de Santa Maria (UFSM) instacron:UFSM |
instname_str |
Universidade Federal de Santa Maria (UFSM) |
instacron_str |
UFSM |
institution |
UFSM |
reponame_str |
Manancial - Repositório Digital da UFSM |
collection |
Manancial - Repositório Digital da UFSM |
repository.name.fl_str_mv |
Manancial - Repositório Digital da UFSM - Universidade Federal de Santa Maria (UFSM) |
repository.mail.fl_str_mv |
atendimento.sib@ufsm.br||tedebc@gmail.com |
_version_ |
1805922045689593856 |