A identidade de Euler e suas constantes
Main Author: | |
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Publication Date: | 2019 |
Format: | Master thesis |
Language: | por |
Source: | Biblioteca Digital de Teses e Dissertações da UFG |
Download full: | http://repositorio.bc.ufg.br/tede/handle/tede/10298 |
Summary: | Teaching math by telling its story can elucidate a series of questions that highlight the need for students to understand the context in which some content is inserted. Such questions may be: who invented mathematics? Why do I need to study this content? In addition, this procedure can be a way of illustration as lessons and motivating students, thus obtaining more significant results in the teaching and learning process. Knowing how mathematics has developed and who its creators and discoverers are critical to making sense of the content of basic education, often taken as done and _nished, as mechanical and without a story that characterizes its discovery or creation. It is in order to bring such elements to this stage of teaching that this paper proposes to objectively report the life and legacy of a brilliant and extremely creative mathematician, Leonhard Euler. As well, emphasize some of his creations present in basic education. It is also proposed to highlight one of his creations, , the identity of Euler, considered one of the most beautiful of all time. Telling the history of this identity, followed by its demonstration and characterization of each of the constants that compose it. |
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Lima, Thaynara Arielly dehttp://lattes.cnpq.br/3324489027928883Lima, Thaynara Arielly deVasconcelos, José Eder Salvador deDias, Ivonildes Ribeiro Martinshttp://lattes.cnpq.br/7701725113616566Reis, Alberto Santos dos2020-01-14T11:58:36Z2019-12-20REIS, A. S. A identidade de Euler e suas constantes. 2019. 47 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2019.http://repositorio.bc.ufg.br/tede/handle/tede/10298Teaching math by telling its story can elucidate a series of questions that highlight the need for students to understand the context in which some content is inserted. Such questions may be: who invented mathematics? Why do I need to study this content? In addition, this procedure can be a way of illustration as lessons and motivating students, thus obtaining more significant results in the teaching and learning process. Knowing how mathematics has developed and who its creators and discoverers are critical to making sense of the content of basic education, often taken as done and _nished, as mechanical and without a story that characterizes its discovery or creation. It is in order to bring such elements to this stage of teaching that this paper proposes to objectively report the life and legacy of a brilliant and extremely creative mathematician, Leonhard Euler. As well, emphasize some of his creations present in basic education. It is also proposed to highlight one of his creations, , the identity of Euler, considered one of the most beautiful of all time. Telling the history of this identity, followed by its demonstration and characterization of each of the constants that compose it.Ensinar matemática contando a sua história pode se elucidar uma série de perguntas que evidenciam a necessidade dos alunos de entender o contexto no qual alguns conteúdos estão inseridos. Tais perguntas podem ser: quem inventou a matemática? Por que preciso estudar esse conteúdo? Além disso, esse procedimento pode ser uma forma de ilustrar as aulas e motivar os alunos, obtendo-se assim resultados mais significativos no processo de ensino e aprendizagem. Saber como a matemática se desenvolveu e quem são seus criadores e descobridores é fundamental para dar sentido aos conteúdos do ensino básico, muitas vezes tido como prontos e acabados, como algo mecânico e sem uma história que caracterize sua descoberta ou criação. É com o intuito de levar tais elementos a esta etapa do ensino que este trabalho se propõe a relatar de forma objetiva a vida e o legado de um matemático brilhante, e extremamente criativo, Leonhard Euler. Bem como, dar ênfase a algumas de suas criações presentes na educação básica. Propõe-se também dar destaque a uma de suas criações, , a identidade de Euler, considerada uma das mais belas de todos os tempos. Contando a história desta identidade, seguida de sua demonstração e caracterização de cada uma das constantes que a compõem.Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2020-01-14T11:14:37Z No. of bitstreams: 2 Dissertação - Mihayr Morais Jardim - 2019.pdf: 1153468 bytes, checksum: e0bd6f958be7077f51710aec04dfd806 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2020-01-14T11:58:36Z (GMT) No. of bitstreams: 2 Dissertação - Mihayr Morais Jardim - 2019.pdf: 1153468 bytes, checksum: e0bd6f958be7077f51710aec04dfd806 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2020-01-14T11:58:36Z (GMT). No. of bitstreams: 2 Dissertação - Mihayr Morais Jardim - 2019.pdf: 1153468 bytes, checksum: e0bd6f958be7077f51710aec04dfd806 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2019-12-20application/pdfporUniversidade Federal de GoiásPROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessLeonhard EulerIdentidade de EulerHistória da MatemáticaLeonhard EulerIdentity of EulerHistory of MathematicsCIENCIAS EXATAS E DA TERRA::MATEMATICAA identidade de Euler e suas constantesEuler's identity and its constantsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis4280721485626151024600600600-4268777512335152015-7090823417984401694reponame:Biblioteca Digital de Teses e Dissertações da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGORIGINALDissertação - Alberto Santos dos Reis - 2019.pdfDissertação - Alberto Santos dos Reis - 2019.pdfapplication/pdf3049327http://repositorio.bc.ufg.br/tede/bitstreams/29b2a150-e284-456c-808c-1bce583f78dc/download37a0b61bbf8e9cd49280c73fdcd8ffaaMD55LICENSElicense.txtlicense.txttext/plain; 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dc.title.eng.fl_str_mv |
A identidade de Euler e suas constantes |
dc.title.alternative.eng.fl_str_mv |
Euler's identity and its constants |
title |
A identidade de Euler e suas constantes |
spellingShingle |
A identidade de Euler e suas constantes Reis, Alberto Santos dos Leonhard Euler Identidade de Euler História da Matemática Leonhard Euler Identity of Euler History of Mathematics CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
A identidade de Euler e suas constantes |
title_full |
A identidade de Euler e suas constantes |
title_fullStr |
A identidade de Euler e suas constantes |
title_full_unstemmed |
A identidade de Euler e suas constantes |
title_sort |
A identidade de Euler e suas constantes |
author |
Reis, Alberto Santos dos |
author_facet |
Reis, Alberto Santos dos |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Lima, Thaynara Arielly de |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/3324489027928883 |
dc.contributor.referee1.fl_str_mv |
Lima, Thaynara Arielly de |
dc.contributor.referee2.fl_str_mv |
Vasconcelos, José Eder Salvador de |
dc.contributor.referee3.fl_str_mv |
Dias, Ivonildes Ribeiro Martins |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/7701725113616566 |
dc.contributor.author.fl_str_mv |
Reis, Alberto Santos dos |
contributor_str_mv |
Lima, Thaynara Arielly de Lima, Thaynara Arielly de Vasconcelos, José Eder Salvador de Dias, Ivonildes Ribeiro Martins |
dc.subject.por.fl_str_mv |
Leonhard Euler Identidade de Euler História da Matemática Leonhard Euler Identity of Euler History of Mathematics |
topic |
Leonhard Euler Identidade de Euler História da Matemática Leonhard Euler Identity of Euler History of Mathematics CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
Teaching math by telling its story can elucidate a series of questions that highlight the need for students to understand the context in which some content is inserted. Such questions may be: who invented mathematics? Why do I need to study this content? In addition, this procedure can be a way of illustration as lessons and motivating students, thus obtaining more significant results in the teaching and learning process. Knowing how mathematics has developed and who its creators and discoverers are critical to making sense of the content of basic education, often taken as done and _nished, as mechanical and without a story that characterizes its discovery or creation. It is in order to bring such elements to this stage of teaching that this paper proposes to objectively report the life and legacy of a brilliant and extremely creative mathematician, Leonhard Euler. As well, emphasize some of his creations present in basic education. It is also proposed to highlight one of his creations, , the identity of Euler, considered one of the most beautiful of all time. Telling the history of this identity, followed by its demonstration and characterization of each of the constants that compose it. |
publishDate |
2019 |
dc.date.issued.fl_str_mv |
2019-12-20 |
dc.date.accessioned.fl_str_mv |
2020-01-14T11:58:36Z |
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 |
REIS, A. S. A identidade de Euler e suas constantes. 2019. 47 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2019. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/10298 |
identifier_str_mv |
REIS, A. S. A identidade de Euler e suas constantes. 2019. 47 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2019. |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/10298 |
dc.language.iso.fl_str_mv |
por |
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por |
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600 600 600 |
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-7090823417984401694 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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Universidade Federal de Goiás |
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PROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matemática (IME) |
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UFG |
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Brasil |
dc.publisher.department.fl_str_mv |
Instituto de Matemática e Estatística - IME (RG) |
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Universidade Federal de Goiás |
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