O problema da trissecção
Autor(a) principal: | |
---|---|
Data de Publicação: | 2018 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações do UFSM |
Texto Completo: | http://repositorio.ufsm.br/handle/1/16291 |
Resumo: | In the history of mathematics some problems had special significance for the influence they exerted in this development. Among these, we mention the classical Greek problems related to construction with a non-graduated ruler and compass. In this work we will discuss these problems, giving special focus to the trisection of the angle. These problems challenged the intellectual power of many mathematicians and intellectuals for a long time, and it was only in the nineteenth century that the impossibility of this construction, using only a non-graduated ruler and compass, was demonstrated. The objective of this work is to present these problems, to discuss their impossibility of resolution and to present, in the special case of the trisection problem, possible resolutions using other instruments. We also present a technique to approach the problem of angle trisection through Origami, which can be used in the classroom. |
id |
UFSM_ee9c90f421243f10cdab5b60a1f488ae |
---|---|
oai_identifier_str |
oai:repositorio.ufsm.br:1/16291 |
network_acronym_str |
UFSM |
network_name_str |
Biblioteca Digital de Teses e Dissertações do UFSM |
repository_id_str |
|
spelling |
2019-04-23T14:12:56Z2019-04-23T14:12:56Z2018-08-27http://repositorio.ufsm.br/handle/1/16291In the history of mathematics some problems had special significance for the influence they exerted in this development. Among these, we mention the classical Greek problems related to construction with a non-graduated ruler and compass. In this work we will discuss these problems, giving special focus to the trisection of the angle. These problems challenged the intellectual power of many mathematicians and intellectuals for a long time, and it was only in the nineteenth century that the impossibility of this construction, using only a non-graduated ruler and compass, was demonstrated. The objective of this work is to present these problems, to discuss their impossibility of resolution and to present, in the special case of the trisection problem, possible resolutions using other instruments. We also present a technique to approach the problem of angle trisection through Origami, which can be used in the classroom.Na história da matemática alguns problemas tiveram um significado especial pela influência que exerceram no seu desenvolvimento. Dentre esses, citamos os problemas clássicos gregos relacionados à construção com régua não graduada e compasso. Neste trabalho discutiremos esses problemas, dando enfoque especial ao da trissecção do ângulo. Esses problemas desafiaram o poder intelectual de vários matemáticos e intelectuais durante muito tempo, e somente no século XIX demonstrou-se a impossibilidade dessa construção utilizando-se apenas régua não graduada e compasso. O objetivo deste trabalho é apresentar esses problemas, discutir sua impossibilidade de resolução e apresentar, no caso especial do problema da trissecção, resoluções possíveis utilizando-se outros instrumentos. Apresentamos também uma técnica de abordagem do problema da trissecção do ângulo através do Origami, que pode ser utilizada em sala de aula.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESporUniversidade 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/openAccessOrigamiTrissecção do ânguloProblemas gregosGeometria de construçãoAngle trisectionGreek puzzlesConstruction geometryCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAO problema da trissecçãoThe trisection probleminfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisPansonato, Claudia Candidahttp://lattes.cnpq.br/5048965212765046Cesca Filho, Vitalinohttp://lattes.cnpq.br/0048422446197920Mathias, Carmen Vieirahttp://lattes.cnpq.br/0112509701698645http://lattes.cnpq.br/5793485138750580Dellaquila, Allan Jeronymo100100000008600088433c9-b4e9-4409-a4ea-444a0bc9f184b7ee169c-0913-4082-9b32-c55841b4441774d495de-c9e9-49f6-a3a9-e93dc7d16cc361725bb3-72e9-42c8-9cfe-0e6e40455f2areponame:Biblioteca Digital de Teses e Dissertações do UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMORIGINALDIS_PPGMRN_2018_DELLAQUILA_ALLAN.pdfDIS_PPGMRN_2018_DELLAQUILA_ALLAN.pdfDissertação de Mestradoapplication/pdf2036499http://repositorio.ufsm.br/bitstream/1/16291/1/DIS_PPGMRN_2018_DELLAQUILA_ALLAN.pdfb247566f7343ace74c52973ce2c3d3d9MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.ufsm.br/bitstream/1/16291/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81956http://repositorio.ufsm.br/bitstream/1/16291/3/license.txt2f0571ecee68693bd5cd3f17c1e075dfMD53TEXTDIS_PPGMRN_2018_DELLAQUILA_ALLAN.pdf.txtDIS_PPGMRN_2018_DELLAQUILA_ALLAN.pdf.txtExtracted texttext/plain79489http://repositorio.ufsm.br/bitstream/1/16291/4/DIS_PPGMRN_2018_DELLAQUILA_ALLAN.pdf.txtadb8794b2dac4e348df4422a80f6bc1aMD54THUMBNAILDIS_PPGMRN_2018_DELLAQUILA_ALLAN.pdf.jpgDIS_PPGMRN_2018_DELLAQUILA_ALLAN.pdf.jpgIM Thumbnailimage/jpeg3942http://repositorio.ufsm.br/bitstream/1/16291/5/DIS_PPGMRN_2018_DELLAQUILA_ALLAN.pdf.jpgfd45962c2b1f018e20ce286dad233149MD551/162912019-04-24 03:01:33.635oai:repositorio.ufsm.br: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 Digital de Teses e Dissertaçõeshttps://repositorio.ufsm.br/ONGhttps://repositorio.ufsm.br/oai/requestatendimento.sib@ufsm.br||tedebc@gmail.comopendoar:2019-04-24T06:01:33Biblioteca Digital de Teses e Dissertações do UFSM - Universidade Federal de Santa Maria (UFSM)false |
dc.title.por.fl_str_mv |
O problema da trissecção |
dc.title.alternative.eng.fl_str_mv |
The trisection problem |
title |
O problema da trissecção |
spellingShingle |
O problema da trissecção Dellaquila, Allan Jeronymo Origami Trissecção do ângulo Problemas gregos Geometria de construção Angle trisection Greek puzzles Construction geometry CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
O problema da trissecção |
title_full |
O problema da trissecção |
title_fullStr |
O problema da trissecção |
title_full_unstemmed |
O problema da trissecção |
title_sort |
O problema da trissecção |
author |
Dellaquila, Allan Jeronymo |
author_facet |
Dellaquila, Allan Jeronymo |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Pansonato, Claudia Candida |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/5048965212765046 |
dc.contributor.referee1.fl_str_mv |
Cesca Filho, Vitalino |
dc.contributor.referee1Lattes.fl_str_mv |
http://lattes.cnpq.br/0048422446197920 |
dc.contributor.referee2.fl_str_mv |
Mathias, Carmen Vieira |
dc.contributor.referee2Lattes.fl_str_mv |
http://lattes.cnpq.br/0112509701698645 |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/5793485138750580 |
dc.contributor.author.fl_str_mv |
Dellaquila, Allan Jeronymo |
contributor_str_mv |
Pansonato, Claudia Candida Cesca Filho, Vitalino Mathias, Carmen Vieira |
dc.subject.por.fl_str_mv |
Origami Trissecção do ângulo Problemas gregos Geometria de construção |
topic |
Origami Trissecção do ângulo Problemas gregos Geometria de construção Angle trisection Greek puzzles Construction geometry CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Angle trisection Greek puzzles Construction geometry |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
In the history of mathematics some problems had special significance for the influence they exerted in this development. Among these, we mention the classical Greek problems related to construction with a non-graduated ruler and compass. In this work we will discuss these problems, giving special focus to the trisection of the angle. These problems challenged the intellectual power of many mathematicians and intellectuals for a long time, and it was only in the nineteenth century that the impossibility of this construction, using only a non-graduated ruler and compass, was demonstrated. The objective of this work is to present these problems, to discuss their impossibility of resolution and to present, in the special case of the trisection problem, possible resolutions using other instruments. We also present a technique to approach the problem of angle trisection through Origami, which can be used in the classroom. |
publishDate |
2018 |
dc.date.issued.fl_str_mv |
2018-08-27 |
dc.date.accessioned.fl_str_mv |
2019-04-23T14:12:56Z |
dc.date.available.fl_str_mv |
2019-04-23T14:12:56Z |
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/1/16291 |
url |
http://repositorio.ufsm.br/handle/1/16291 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.cnpq.fl_str_mv |
100100000008 |
dc.relation.confidence.fl_str_mv |
600 |
dc.relation.authority.fl_str_mv |
088433c9-b4e9-4409-a4ea-444a0bc9f184 b7ee169c-0913-4082-9b32-c55841b44417 74d495de-c9e9-49f6-a3a9-e93dc7d16cc3 61725bb3-72e9-42c8-9cfe-0e6e40455f2a |
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:Biblioteca Digital de Teses e Dissertações do 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 |
Biblioteca Digital de Teses e Dissertações do UFSM |
collection |
Biblioteca Digital de Teses e Dissertações do UFSM |
bitstream.url.fl_str_mv |
http://repositorio.ufsm.br/bitstream/1/16291/1/DIS_PPGMRN_2018_DELLAQUILA_ALLAN.pdf http://repositorio.ufsm.br/bitstream/1/16291/2/license_rdf http://repositorio.ufsm.br/bitstream/1/16291/3/license.txt http://repositorio.ufsm.br/bitstream/1/16291/4/DIS_PPGMRN_2018_DELLAQUILA_ALLAN.pdf.txt http://repositorio.ufsm.br/bitstream/1/16291/5/DIS_PPGMRN_2018_DELLAQUILA_ALLAN.pdf.jpg |
bitstream.checksum.fl_str_mv |
b247566f7343ace74c52973ce2c3d3d9 4460e5956bc1d1639be9ae6146a50347 2f0571ecee68693bd5cd3f17c1e075df adb8794b2dac4e348df4422a80f6bc1a fd45962c2b1f018e20ce286dad233149 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações do UFSM - Universidade Federal de Santa Maria (UFSM) |
repository.mail.fl_str_mv |
atendimento.sib@ufsm.br||tedebc@gmail.com |
_version_ |
1801485206121611264 |