Solução dos três problemas clássicos da matemática grega por curvas mecânicas
Autor(a) principal: | |
---|---|
Data de Publicação: | 2014 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional Manancial 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. |
id |
UFSM-20_d13ece16f3a85f90312f910bd1cf3e1e |
---|---|
oai_identifier_str |
oai:repositorio.ufsm.br:1/21532 |
network_acronym_str |
UFSM-20 |
network_name_str |
Repositório Institucional Manancial UFSM |
repository_id_str |
3913 |
spelling |
2021-07-20T19:05:01Z2021-07-20T19:05:01Z2014-08-29http://repositorio.ufsm.br/handle/1/21532This 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.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/openAccessGeometriaProblemas cl ássicosQuadratura do c írculoTrissecção do ânguloDuplicação do cuboGeometryClassical problemsSquaring the circleTrisection angleDoubling the cubeCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICASolução dos três problemas clássicos da matemática grega por curvas mecânicasSolution of the three classical problems of the greek mathematics with mechanical curvesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisFigueiredo, Edson Sidneyhttp://lattes.cnpq.br/1112919781647346Gomes, DenilsonBinotto, Rosane RossatoXXXXXXXXXXXXXXXXD'Acampora, Raphael10010000000860060060007cc44c6-bbcf-4946-82b0-f87e4536387bc4f2a45c-d6e2-4e28-8e5e-8d9c8cd6ca37f211a39c-c71d-43e4-b152-2e2d783233e9ee198c23-9dd0-46bd-b505-feb8c904f0e6reponame:Repositório Institucional Manancial UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMORIGINALDIS_PPGMRN_2014_D' ACAMPORA_RAPHAEL.pdfDIS_PPGMRN_2014_D' ACAMPORA_RAPHAEL.pdfDissertação de Mestradoapplication/pdf1802764http://repositorio.ufsm.br/bitstream/1/21532/1/DIS_PPGMRN_2014_D%27%20ACAMPORA_RAPHAEL.pdf91dd8ea6c9fd35097f202de48325f6cfMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.ufsm.br/bitstream/1/21532/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81956http://repositorio.ufsm.br/bitstream/1/21532/3/license.txt2f0571ecee68693bd5cd3f17c1e075dfMD53TEXTDIS_PPGMRN_2014_D' ACAMPORA_RAPHAEL.pdf.txtDIS_PPGMRN_2014_D' ACAMPORA_RAPHAEL.pdf.txtExtracted texttext/plain93547http://repositorio.ufsm.br/bitstream/1/21532/4/DIS_PPGMRN_2014_D%27%20ACAMPORA_RAPHAEL.pdf.txt3dd13ff60210bfa29e99aa81e99d556bMD54THUMBNAILDIS_PPGMRN_2014_D' ACAMPORA_RAPHAEL.pdf.jpgDIS_PPGMRN_2014_D' ACAMPORA_RAPHAEL.pdf.jpgIM Thumbnailimage/jpeg5133http://repositorio.ufsm.br/bitstream/1/21532/5/DIS_PPGMRN_2014_D%27%20ACAMPORA_RAPHAEL.pdf.jpg7eb5019a1c0d3d52cd4d998262ee1556MD551/215322021-07-21 03:02:12.786oai:repositorio.ufsm.br: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ório Institucionalhttp://repositorio.ufsm.br/PUBhttp://repositorio.ufsm.br/oai/requestouvidoria@ufsm.bropendoar:39132021-07-21T06:02:12Repositório Institucional Manancial UFSM - Universidade Federal de Santa Maria (UFSM)false |
dc.title.por.fl_str_mv |
Solução dos três problemas clássicos da matemática grega por curvas mecânicas |
dc.title.alternative.eng.fl_str_mv |
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.advisor1.fl_str_mv |
Figueiredo, Edson Sidney |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/1112919781647346 |
dc.contributor.referee1.fl_str_mv |
Gomes, Denilson |
dc.contributor.referee2.fl_str_mv |
Binotto, Rosane Rossato |
dc.contributor.authorLattes.fl_str_mv |
XXXXXXXXXXXXXXXX |
dc.contributor.author.fl_str_mv |
D'Acampora, Raphael |
contributor_str_mv |
Figueiredo, Edson Sidney Gomes, Denilson Binotto, Rosane Rossato |
dc.subject.por.fl_str_mv |
Geometria Problemas cl ássicos Quadratura do c írculo Trissecção do ângulo Duplicação do cubo |
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 |
dc.subject.eng.fl_str_mv |
Geometry Classical problems Squaring the circle Trisection angle Doubling the cube |
dc.subject.cnpq.fl_str_mv |
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.issued.fl_str_mv |
2014-08-29 |
dc.date.accessioned.fl_str_mv |
2021-07-20T19:05:01Z |
dc.date.available.fl_str_mv |
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.relation.cnpq.fl_str_mv |
100100000008 |
dc.relation.confidence.fl_str_mv |
600 600 600 |
dc.relation.authority.fl_str_mv |
07cc44c6-bbcf-4946-82b0-f87e4536387b c4f2a45c-d6e2-4e28-8e5e-8d9c8cd6ca37 f211a39c-c71d-43e4-b152-2e2d783233e9 ee198c23-9dd0-46bd-b505-feb8c904f0e6 |
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:Repositório Institucional Manancial 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 |
Repositório Institucional Manancial UFSM |
collection |
Repositório Institucional Manancial UFSM |
bitstream.url.fl_str_mv |
http://repositorio.ufsm.br/bitstream/1/21532/1/DIS_PPGMRN_2014_D%27%20ACAMPORA_RAPHAEL.pdf http://repositorio.ufsm.br/bitstream/1/21532/2/license_rdf http://repositorio.ufsm.br/bitstream/1/21532/3/license.txt http://repositorio.ufsm.br/bitstream/1/21532/4/DIS_PPGMRN_2014_D%27%20ACAMPORA_RAPHAEL.pdf.txt http://repositorio.ufsm.br/bitstream/1/21532/5/DIS_PPGMRN_2014_D%27%20ACAMPORA_RAPHAEL.pdf.jpg |
bitstream.checksum.fl_str_mv |
91dd8ea6c9fd35097f202de48325f6cf 4460e5956bc1d1639be9ae6146a50347 2f0571ecee68693bd5cd3f17c1e075df 3dd13ff60210bfa29e99aa81e99d556b 7eb5019a1c0d3d52cd4d998262ee1556 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional Manancial UFSM - Universidade Federal de Santa Maria (UFSM) |
repository.mail.fl_str_mv |
ouvidoria@ufsm.br |
_version_ |
1808854724682711040 |