Coordenadas baricêntricas
| Ano de defesa: | 2018 |
|---|---|
| Autor(a) principal: | |
| Orientador(a): | |
| Banca de defesa: | |
| Tipo de documento: | Dissertação |
| Tipo de acesso: | Acesso aberto |
| Idioma: | por |
| Instituição de defesa: |
Não Informado pela instituição
|
| Programa de Pós-Graduação: |
Não Informado pela instituição
|
| Departamento: |
Não Informado pela instituição
|
| País: |
Não Informado pela instituição
|
| Palavras-chave em Português: | |
| Link de acesso: | http://www.repositorio.ufc.br/handle/riufc/40048 |
Resumo: | The objective of this work is to present the technique of solving problems of geometry plane called barycentric coordinates and show that the solutions to some problems become easier with the use of this technique. We begin the work with the development of the basic theory of this technique, from the definition of barycentric coordinates and the calculation of the barycentric coordinates of some remarkable points of the triangle, passing through the equation of the line, formula of the distance between two points, Conway notation and conditions of parallelism and perpendicularity. After that, we apply this technique to solve some problems, many of them coming from Olympic competitions of Matemática. We finish the work indicating a possibility of insertion of this subject in the high school curriculum. |
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Ferreira, José Clairto RochaGirão, Frederico Vale2019-02-28T15:39:54Z2019-02-28T15:39:54Z2018FERREIRA, José Clairto Rocha. Coordenadas baricêntricas. 2018. 61 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, 2018.http://www.repositorio.ufc.br/handle/riufc/40048The objective of this work is to present the technique of solving problems of geometry plane called barycentric coordinates and show that the solutions to some problems become easier with the use of this technique. We begin the work with the development of the basic theory of this technique, from the definition of barycentric coordinates and the calculation of the barycentric coordinates of some remarkable points of the triangle, passing through the equation of the line, formula of the distance between two points, Conway notation and conditions of parallelism and perpendicularity. After that, we apply this technique to solve some problems, many of them coming from Olympic competitions of Matemática. We finish the work indicating a possibility of insertion of this subject in the high school curriculum.O objetivo deste trabalho é apresentar a técnica de resolução de problemas de geometria plana chamada coordenadas baricêntricas e mostrar que as soluções de alguns problemas tornam-se mais simples com o uso desta técnica. Iniciamos o trabalho com o desenvolvimento da teoria básica desta técnica, desde a definição de coordenadas baricêntricas e do cálculo das coordenadas baricêntricas de alguns pontos notáveis do triângulo, passando pela equação da reta, fórmula da distância entre dois pontos, notação de Conway e condições de paralelismo e perpendicularidade. Depois disso, aplicamos esta técnica para resolver alguns problemas, muitos deles oriundos de competições olímpicas de Matemática. Finalizamos o trabalho indicando uma possibilidade da inserção deste assunto no currículo do ensino médio.Coordenadas baricêntricasBaricentric coordinatesGeometria analíticaAnalytical GeometryGeometria plana - Resolução de problemasFlat geometry - TroubleshootingCoordenadas baricêntricasBaricentric coordinatesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisporreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCinfo:eu-repo/semantics/openAccessLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.ufc.br/bitstream/riufc/40048/5/license.txt8a4605be74aa9ea9d79846c1fba20a33MD55ORIGINAL2018_dis_jcrferreira.pdf2018_dis_jcrferreira.pdfapplication/pdf1192493http://repositorio.ufc.br/bitstream/riufc/40048/4/2018_dis_jcrferreira.pdf982cf310270db57bb721fcff24229d75MD54riufc/400482019-03-01 10:30:49.542oai:repositorio.ufc.br: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Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2019-03-01T13:30:49Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false |
| dc.title.pt_BR.fl_str_mv |
Coordenadas baricêntricas |
| dc.title.en.pt_BR.fl_str_mv |
Baricentric coordinates |
| title |
Coordenadas baricêntricas |
| spellingShingle |
Coordenadas baricêntricas Ferreira, José Clairto Rocha Coordenadas baricêntricas Baricentric coordinates Geometria analítica Analytical Geometry Geometria plana - Resolução de problemas Flat geometry - Troubleshooting |
| title_short |
Coordenadas baricêntricas |
| title_full |
Coordenadas baricêntricas |
| title_fullStr |
Coordenadas baricêntricas |
| title_full_unstemmed |
Coordenadas baricêntricas |
| title_sort |
Coordenadas baricêntricas |
| author |
Ferreira, José Clairto Rocha |
| author_facet |
Ferreira, José Clairto Rocha |
| author_role |
author |
| dc.contributor.author.fl_str_mv |
Ferreira, José Clairto Rocha |
| dc.contributor.advisor1.fl_str_mv |
Girão, Frederico Vale |
| contributor_str_mv |
Girão, Frederico Vale |
| dc.subject.por.fl_str_mv |
Coordenadas baricêntricas Baricentric coordinates Geometria analítica Analytical Geometry Geometria plana - Resolução de problemas Flat geometry - Troubleshooting |
| topic |
Coordenadas baricêntricas Baricentric coordinates Geometria analítica Analytical Geometry Geometria plana - Resolução de problemas Flat geometry - Troubleshooting |
| description |
The objective of this work is to present the technique of solving problems of geometry plane called barycentric coordinates and show that the solutions to some problems become easier with the use of this technique. We begin the work with the development of the basic theory of this technique, from the definition of barycentric coordinates and the calculation of the barycentric coordinates of some remarkable points of the triangle, passing through the equation of the line, formula of the distance between two points, Conway notation and conditions of parallelism and perpendicularity. After that, we apply this technique to solve some problems, many of them coming from Olympic competitions of Matemática. We finish the work indicating a possibility of insertion of this subject in the high school curriculum. |
| publishDate |
2018 |
| dc.date.issued.fl_str_mv |
2018 |
| dc.date.accessioned.fl_str_mv |
2019-02-28T15:39:54Z |
| dc.date.available.fl_str_mv |
2019-02-28T15:39:54Z |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/masterThesis |
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masterThesis |
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publishedVersion |
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FERREIRA, José Clairto Rocha. Coordenadas baricêntricas. 2018. 61 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, 2018. |
| dc.identifier.uri.fl_str_mv |
http://www.repositorio.ufc.br/handle/riufc/40048 |
| identifier_str_mv |
FERREIRA, José Clairto Rocha. Coordenadas baricêntricas. 2018. 61 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, 2018. |
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http://www.repositorio.ufc.br/handle/riufc/40048 |
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por |
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por |
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openAccess |
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