From the myth of Euclidean Geometry to the teaching of Non-Euclidean Geometry
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2010 |
| Outros Autores: | |
| Tipo de documento: | Artigo |
| Idioma: | por |
| Título da fonte: | Vértices (Campos dos Goitacazes. Online) |
| Texto Completo: | https://editoraessentia.iff.edu.br/index.php/vertices/article/view/1809-2667.20070007 |
Resumo: | Non-Euclidean Geometry originated from unsuccessful attempts to prove that Euclid’s fifth postulate was a theorem. From the first four Euclidean postulates and the negation of the fifth derived other geometries whose postulates are possible in planes models, and as consistent as that in Euclidean Geometry. This article presents the Elliptical and Hyperbolic Geometry models with their postulates and concepts. A discussion of the teaching and learning of these geometries is also presented. |
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From the myth of Euclidean Geometry to the teaching of Non-Euclidean GeometryDo mito da Geometria Euclidiana ao ensino das Geometrias Não EuclidianasEuclidean GeometryEuclid’s fifth postulateTeaching and LearningNon- Euclidean GeometryGeometria EuclidianaQuinto postulado de EuclidesEnsino e aprendizagem de Geometrias Não EuclidianasNon-Euclidean Geometry originated from unsuccessful attempts to prove that Euclid’s fifth postulate was a theorem. From the first four Euclidean postulates and the negation of the fifth derived other geometries whose postulates are possible in planes models, and as consistent as that in Euclidean Geometry. This article presents the Elliptical and Hyperbolic Geometry models with their postulates and concepts. A discussion of the teaching and learning of these geometries is also presented.Das tentativas frustradas de provar que o quinto postulado de Euclides era um teorema, surgiram as Geometrias Não Euclidianas. Com os quatro primeiros postulados de Euclides e a negação do quinto, surgiram outras Geometrias cujos postulados são possíveis em modelos planos que são tão consistentes quanto o da Geometria Euclidiana. Neste artigo são apresentados os modelos, postulados e conceitos da Geometria Elíptica e Geometria Hiperbólica. Além disso, é discutido o ensino dessas Geometrias.Instituto Federal de Educação, Ciência e Tecnologia Fluminense2010-05-13info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://editoraessentia.iff.edu.br/index.php/vertices/article/view/1809-2667.2007000710.5935/1809-2667.20070007Revista Vértices; Vol. 9 No. 1/3 (2007): Edição comemorativa - 10 anos; 73-82Revista Vértices; Vol. 9 Núm. 1/3 (2007): Edição comemorativa - 10 anos; 73-82Revista Vértices; v. 9 n. 1/3 (2007): Edição comemorativa - 10 anos; 73-821809-26671415-2843reponame:Vértices (Campos dos Goitacazes. Online)instname:Centro Federal de Educação Tecnológica de Campos dos Goytacazesinstacron:IFFluminenseporhttps://editoraessentia.iff.edu.br/index.php/vertices/article/view/1809-2667.20070007/41Barreto, Mylane dos SantosTavares, Salvadorinfo:eu-repo/semantics/openAccess2022-01-25T09:01:17Zoai:ojs.editoraessentia.iff.edu.br:article/53Revistahttps://essentiaeditora.iff.edu.br/index.php/vertices/PUBhttps://essentiaeditora.iff.edu.br/index.php/vertices/oaiessentia@iff.edu.br1809-26671415-2843opendoar:2022-01-25T09:01:17Vértices (Campos dos Goitacazes. Online) - Centro Federal de Educação Tecnológica de Campos dos Goytacazesfalse |
| dc.title.none.fl_str_mv |
From the myth of Euclidean Geometry to the teaching of Non-Euclidean Geometry Do mito da Geometria Euclidiana ao ensino das Geometrias Não Euclidianas |
| title |
From the myth of Euclidean Geometry to the teaching of Non-Euclidean Geometry |
| spellingShingle |
From the myth of Euclidean Geometry to the teaching of Non-Euclidean Geometry Barreto, Mylane dos Santos Euclidean Geometry Euclid’s fifth postulate Teaching and Learning Non- Euclidean Geometry Geometria Euclidiana Quinto postulado de Euclides Ensino e aprendizagem de Geometrias Não Euclidianas |
| title_short |
From the myth of Euclidean Geometry to the teaching of Non-Euclidean Geometry |
| title_full |
From the myth of Euclidean Geometry to the teaching of Non-Euclidean Geometry |
| title_fullStr |
From the myth of Euclidean Geometry to the teaching of Non-Euclidean Geometry |
| title_full_unstemmed |
From the myth of Euclidean Geometry to the teaching of Non-Euclidean Geometry |
| title_sort |
From the myth of Euclidean Geometry to the teaching of Non-Euclidean Geometry |
| author |
Barreto, Mylane dos Santos |
| author_facet |
Barreto, Mylane dos Santos Tavares, Salvador |
| author_role |
author |
| author2 |
Tavares, Salvador |
| author2_role |
author |
| dc.contributor.author.fl_str_mv |
Barreto, Mylane dos Santos Tavares, Salvador |
| dc.subject.por.fl_str_mv |
Euclidean Geometry Euclid’s fifth postulate Teaching and Learning Non- Euclidean Geometry Geometria Euclidiana Quinto postulado de Euclides Ensino e aprendizagem de Geometrias Não Euclidianas |
| topic |
Euclidean Geometry Euclid’s fifth postulate Teaching and Learning Non- Euclidean Geometry Geometria Euclidiana Quinto postulado de Euclides Ensino e aprendizagem de Geometrias Não Euclidianas |
| description |
Non-Euclidean Geometry originated from unsuccessful attempts to prove that Euclid’s fifth postulate was a theorem. From the first four Euclidean postulates and the negation of the fifth derived other geometries whose postulates are possible in planes models, and as consistent as that in Euclidean Geometry. This article presents the Elliptical and Hyperbolic Geometry models with their postulates and concepts. A discussion of the teaching and learning of these geometries is also presented. |
| publishDate |
2010 |
| dc.date.none.fl_str_mv |
2010-05-13 |
| dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.uri.fl_str_mv |
https://editoraessentia.iff.edu.br/index.php/vertices/article/view/1809-2667.20070007 10.5935/1809-2667.20070007 |
| url |
https://editoraessentia.iff.edu.br/index.php/vertices/article/view/1809-2667.20070007 |
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10.5935/1809-2667.20070007 |
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por |
| language |
por |
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https://editoraessentia.iff.edu.br/index.php/vertices/article/view/1809-2667.20070007/41 |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
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Instituto Federal de Educação, Ciência e Tecnologia Fluminense |
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Instituto Federal de Educação, Ciência e Tecnologia Fluminense |
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Revista Vértices; Vol. 9 No. 1/3 (2007): Edição comemorativa - 10 anos; 73-82 Revista Vértices; Vol. 9 Núm. 1/3 (2007): Edição comemorativa - 10 anos; 73-82 Revista Vértices; v. 9 n. 1/3 (2007): Edição comemorativa - 10 anos; 73-82 1809-2667 1415-2843 reponame:Vértices (Campos dos Goitacazes. Online) instname:Centro Federal de Educação Tecnológica de Campos dos Goytacazes instacron:IFFluminense |
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Centro Federal de Educação Tecnológica de Campos dos Goytacazes |
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IFFluminense |
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IFFluminense |
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Vértices (Campos dos Goitacazes. Online) |
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Vértices (Campos dos Goitacazes. Online) |
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Vértices (Campos dos Goitacazes. Online) - Centro Federal de Educação Tecnológica de Campos dos Goytacazes |
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essentia@iff.edu.br |
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