Proofs and generalizations of the pythagorean theorem
This article explores a topic developed by a group of researchers of the Science and Technology Teaching School of Instituto Federal de Pernambuco, Brazil (IFPE), in assistance to the development of the Mathematics Practical and Teaching Laboratory of the distance learning Teaching Licensure, financ...
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| Format: | Online |
| Language: | spa |
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Universidad Pedagógica y Tecnológica de Colombia
2011
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| Online Access: | https://revistas.uptc.edu.co/index.php/praxis_saber/article/view/1112 |
| _version_ | 1802223951866232832 |
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| author | Cavalcanti, Lialda B. de Arimatéa Roch, Cristiane |
| author_facet | Cavalcanti, Lialda B. de Arimatéa Roch, Cristiane |
| author_sort | Cavalcanti, Lialda B. |
| collection | OJS |
| description | This article explores a topic developed by a group of researchers of the Science and Technology Teaching School of Instituto Federal de Pernambuco, Brazil (IFPE), in assistance to the development of the Mathematics Practical and Teaching Laboratory of the distance learning Teaching Licensure, financed by the Universidad Abierta de Brasil. In this article, we describe the peculiarities present in the proofs of the Pythagorean theorem with the purpose of illustrating some of these methods. The selection of these peculiarities was founded and based on the comparison of areas by means of the superimposition of geometrical shapes and used several different class resources. Some generalizations of this important theorem in mathematical problem-solving are also shown. |
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-1112 |
| institution | Revista Praxis & Saber |
| language | spa |
| publishDate | 2011 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-11122019-02-26T15:01:45Z Proofs and generalizations of the pythagorean theorem Demostraciones y generalizaciones del teorema de pitágoras Démonstrations et généralisation du théorème de pythagore Demonstrações egeneralizações do teorema de Pitágoras Cavalcanti, Lialda B. de Arimatéa Roch, Cristiane pythagorean theorem geometric shapes proofs generalizations. Teorema de Pitágoras figuras geométricas demostraciones generalizaciones. Théorème de Pythagore figures géométriques démonstrations généralisations. Teorema de Pitágoras figuras geométricas demonstrações generalizações. This article explores a topic developed by a group of researchers of the Science and Technology Teaching School of Instituto Federal de Pernambuco, Brazil (IFPE), in assistance to the development of the Mathematics Practical and Teaching Laboratory of the distance learning Teaching Licensure, financed by the Universidad Abierta de Brasil. In this article, we describe the peculiarities present in the proofs of the Pythagorean theorem with the purpose of illustrating some of these methods. The selection of these peculiarities was founded and based on the comparison of areas by means of the superimposition of geometrical shapes and used several different class resources. Some generalizations of this important theorem in mathematical problem-solving are also shown. Este artículo aborda el tema desarrollado por el grupo de investigadores de Enseñanza de Ciencias y Tecnología del Instituto Federal de Educación de Pernambuco (IFPE) para auxiliar el desarrollo del programa de Laboratorio de Práctica y Enseñanza de la Matemática del curso de licenciatura en la modalidad de educación a distancia, con el apoyo de la Universidad Abierta del Brasil. En este texto describimos peculiaridades contenidas en las demostraciones del Teorema de Pitágoras con el fin de ilustrar algunos de esos métodos. La selección de estas se fundamentó y basó en la comparación de áreas por medio de la superposición de figuras y el uso de diversos recursos en clase. Además se presentan algunas generalizaciones de ese teorema, tan importante en la resolución de problemas en matemáticas. Cet article aborde le sujet développé par le groupe de chercheurs d’Enseignement de Sciences et Technologie de l’Institut Federal de Educación de Pernambuco (IFPE), pour aider au développement du programme du Laboratoire de Stage et Enseignement des Mathématiques du cours de Licence dans la modalité d’éducation `a distance, avec l’appui de l’Université Ouverte du Brésil. Dans ce texte, on décrit des particularités contenues dans les démonstrations du Théorème de Pythagore, en ayant comme but le fait d’illustrer quelques-unes de ces méthodes-là. La sélection de ces particularités-là, a été fondée et basée sur la comparaison des domaines, par le biais de la superposition de figures et l’utilisation de diverses ressources en classe. En plus, on présente des généralisations de ce héorème-là, si important dans la résolution des problèmes en mathématiques. Este artigo aborda tema desenvolvido pelo grupo de pesquisadores de Ensino de Ciência e Tecnologia do Instituto Federal de Educação de Pernambuco (IFPE), para subsidiar ementa da disciplina Laboratório de Prática e Ensino de Matemática do curso de Licenciatura em Matemática na modalidade de Educação à Distância com apoio da Universidade Aberta do Brasil. Neste texto descrevemos peculiaridades contidas nas demonstrações do teorema de Pitágoras a fim de ilustrar alguns desses diferentes métodos. A seleção das mesmas se fundamentou na utilização de aspectos geométricos que se baseiam na comparação de áreas, por meio de superposição de figuras e na viabilidade de recursos diferenciados na sala de aula. Além disso, apresentamos algumas generalizações desse teorema tão importante na resolução de problemas na Matemática. Universidad Pedagógica y Tecnológica de Colombia 2011-01-06 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf https://revistas.uptc.edu.co/index.php/praxis_saber/article/view/1112 Praxis & Saber; Vol. 2 No. 3 (2011): Educación Matemática; 103-118 Praxis & Saber; Vol. 2 Núm. 3 (2011): Educación Matemática; 103-118 Praxis & Saber; Vol. 2 No 3 (2011): Educación Matemática; 103-118 Praxis & Saber; V. 2 N. 3 (2011): Educación Matemática; 103-118 Praxis & Saber; v. 2 n. 3 (2011): Educación Matemática; 103-118 2462-8603 2216-0159 spa https://revistas.uptc.edu.co/index.php/praxis_saber/article/view/1112/1111 |
| spellingShingle | pythagorean theorem geometric shapes proofs generalizations. Teorema de Pitágoras figuras geométricas demostraciones generalizaciones. Théorème de Pythagore figures géométriques démonstrations généralisations. Teorema de Pitágoras figuras geométricas demonstrações generalizações. Cavalcanti, Lialda B. de Arimatéa Roch, Cristiane Proofs and generalizations of the pythagorean theorem |
| title | Proofs and generalizations of the pythagorean theorem |
| title_alt | Demostraciones y generalizaciones del teorema de pitágoras Démonstrations et généralisation du théorème de pythagore Demonstrações egeneralizações do teorema de Pitágoras |
| title_full | Proofs and generalizations of the pythagorean theorem |
| title_fullStr | Proofs and generalizations of the pythagorean theorem |
| title_full_unstemmed | Proofs and generalizations of the pythagorean theorem |
| title_short | Proofs and generalizations of the pythagorean theorem |
| title_sort | proofs and generalizations of the pythagorean theorem |
| topic | pythagorean theorem geometric shapes proofs generalizations. Teorema de Pitágoras figuras geométricas demostraciones generalizaciones. Théorème de Pythagore figures géométriques démonstrations généralisations. Teorema de Pitágoras figuras geométricas demonstrações generalizações. |
| topic_facet | pythagorean theorem geometric shapes proofs generalizations. Teorema de Pitágoras figuras geométricas demostraciones generalizaciones. Théorème de Pythagore figures géométriques démonstrations généralisations. Teorema de Pitágoras figuras geométricas demonstrações generalizações. |
| url | https://revistas.uptc.edu.co/index.php/praxis_saber/article/view/1112 |
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