O Teorema de Pitágoras
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da UFRPE |
Texto Completo: | http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/6289 |
Resumo: | This work is a bibliographical research on the various proofs of the Pythagoras theorem, its applications in solving problems and educational activities used in the classroom, we have also a small historical note about Pythagoras and the Pythagorean school. The proofs covered here are of three types, the rst are the algebraic proofs are based on these metric relations in right triangle, the second are geometric proofs these are based on areas of comparisons and the third vector proofs are based on vector concept and its properties. |
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VERA, Jorge Antonio HinojosaSILVA, Adriano Regis Melo Rodrigues daSOUSA NETO, Vicente Francisco deOLIVEIRA FILHO, Amaro José de2017-02-10T13:01:32Z2016-11-17OLIVEIRA FILHO, Amaro José de. O Teorema de Pitágoras. 2016. 74 f. Dissertação (Programa de Pós-Graduação em Matemática (PROFMAT)) - Universidade Federal Rural de Pernambuco, Recife.http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/6289This work is a bibliographical research on the various proofs of the Pythagoras theorem, its applications in solving problems and educational activities used in the classroom, we have also a small historical note about Pythagoras and the Pythagorean school. The proofs covered here are of three types, the rst are the algebraic proofs are based on these metric relations in right triangle, the second are geometric proofs these are based on areas of comparisons and the third vector proofs are based on vector concept and its properties.A presente dissertação trata de uma pesquisa bibliográfica sobre as diversas demonstrações do Teorema de Pitágoras, suas aplicações na resolução de problemas e atividades didáticas utilizadas em sala de aula, temos também uma pequena nota histórica sobre Pitágoras e a escola pitagórica. As demonstrações aqui abordadas são de três tipos, as primeiras são demonstrações "algébricas", estas são baseadas nas relações métricas no triângulo retângulo, as segundas são demonstrações "geométricas", estas são baseadas em comparações de áreas e as terceiras são demonstrações "vetoriais" baseadas no conceito de vetor e suas propriedades.Submitted by Mario BC (mario@bc.ufrpe.br) on 2017-02-10T13:01:32Z No. of bitstreams: 1 Amaro Jose de Oliveira Filho.pdf: 1941970 bytes, checksum: 77be6fd3d4699b7ac9ae9fded8bae11d (MD5)Made available in DSpace on 2017-02-10T13:01:32Z (GMT). No. of bitstreams: 1 Amaro Jose de Oliveira Filho.pdf: 1941970 bytes, checksum: 77be6fd3d4699b7ac9ae9fded8bae11d (MD5) Previous issue date: 2016-11-17Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfporUniversidade Federal Rural de PernambucoPrograma de Pós-Graduação em Matemática (PROFMAT)UFRPEBrasilDepartamento de MatemáticaTeorema de PitágorasDidáticaEnsino de matemáticaCIENCIAS EXATAS E DA TERRA::MATEMATICAO Teorema de Pitágorasinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis7256355350190039125600600600600-6155401143231123537-70908234179844016942075167498588264571info:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UFRPEinstname:Universidade Federal Rural de Pernambuco (UFRPE)instacron:UFRPELICENSElicense.txtlicense.txttext/plain; charset=utf-82165http://www.tede2.ufrpe.br:8080/tede2/bitstream/tede2/6289/1/license.txtbd3efa91386c1718a7f26a329fdcb468MD51ORIGINALAmaro Jose de Oliveira Filho.pdfAmaro Jose de Oliveira Filho.pdfapplication/pdf1941970http://www.tede2.ufrpe.br:8080/tede2/bitstream/tede2/6289/2/Amaro+Jose+de+Oliveira+Filho.pdf77be6fd3d4699b7ac9ae9fded8bae11dMD52tede2/62892018-08-24 11:30:30.205oai:tede2: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Biblioteca Digital de Teses e Dissertaçõeshttp://www.tede2.ufrpe.br:8080/tede/PUBhttp://www.tede2.ufrpe.br:8080/oai/requestbdtd@ufrpe.br ||bdtd@ufrpe.bropendoar:2024-05-28T12:34:09.225804Biblioteca Digital de Teses e Dissertações da UFRPE - Universidade Federal Rural de Pernambuco (UFRPE)false |
dc.title.por.fl_str_mv |
O Teorema de Pitágoras |
title |
O Teorema de Pitágoras |
spellingShingle |
O Teorema de Pitágoras OLIVEIRA FILHO, Amaro José de Teorema de Pitágoras Didática Ensino de matemática CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
O Teorema de Pitágoras |
title_full |
O Teorema de Pitágoras |
title_fullStr |
O Teorema de Pitágoras |
title_full_unstemmed |
O Teorema de Pitágoras |
title_sort |
O Teorema de Pitágoras |
author |
OLIVEIRA FILHO, Amaro José de |
author_facet |
OLIVEIRA FILHO, Amaro José de |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
VERA, Jorge Antonio Hinojosa |
dc.contributor.referee1.fl_str_mv |
SILVA, Adriano Regis Melo Rodrigues da |
dc.contributor.referee2.fl_str_mv |
SOUSA NETO, Vicente Francisco de |
dc.contributor.author.fl_str_mv |
OLIVEIRA FILHO, Amaro José de |
contributor_str_mv |
VERA, Jorge Antonio Hinojosa SILVA, Adriano Regis Melo Rodrigues da SOUSA NETO, Vicente Francisco de |
dc.subject.por.fl_str_mv |
Teorema de Pitágoras Didática Ensino de matemática |
topic |
Teorema de Pitágoras Didática Ensino de matemática CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This work is a bibliographical research on the various proofs of the Pythagoras theorem, its applications in solving problems and educational activities used in the classroom, we have also a small historical note about Pythagoras and the Pythagorean school. The proofs covered here are of three types, the rst are the algebraic proofs are based on these metric relations in right triangle, the second are geometric proofs these are based on areas of comparisons and the third vector proofs are based on vector concept and its properties. |
publishDate |
2016 |
dc.date.issued.fl_str_mv |
2016-11-17 |
dc.date.accessioned.fl_str_mv |
2017-02-10T13:01:32Z |
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.citation.fl_str_mv |
OLIVEIRA FILHO, Amaro José de. O Teorema de Pitágoras. 2016. 74 f. Dissertação (Programa de Pós-Graduação em Matemática (PROFMAT)) - Universidade Federal Rural de Pernambuco, Recife. |
dc.identifier.uri.fl_str_mv |
http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/6289 |
identifier_str_mv |
OLIVEIRA FILHO, Amaro José de. O Teorema de Pitágoras. 2016. 74 f. Dissertação (Programa de Pós-Graduação em Matemática (PROFMAT)) - Universidade Federal Rural de Pernambuco, Recife. |
url |
http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/6289 |
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