Conjunto de Mandelbrot

Detalhes bibliográficos
Ano de defesa: 2016
Autor(a) principal: Reis, Márcio Vaiz dos lattes
Orientador(a): Vieira, Ewerton Rocha lattes
Banca de defesa: Vieira, Ewerton Rocha, Lima, Lidiane dos Santos Monteiro de, Vasconcelos, José Eder Salvador de
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal de Goiás
Programa de Pós-Graduação: PROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matemática (IME)
Departamento: Instituto de Matemática e Estatística - IME (RG)
País: Brasil
Palavras-chave em Português:
Geometria fractal
Conjunto de Mandelbrot
Conjunto de Julia e Geogebra
Fractal geometry
Mandelbrot set
Julia set and Geogebra
Área do conhecimento CNPq:
CIENCIAS EXATAS E DA TERRA::MATEMATICA
Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/6343
Resumo: The purpose of this dissertation is to present an introductory approach to the complex dynamics and fractal geometry, especially the Mandelbrot set. With the goal to simplify and stimulate the introduction of complex number in high school, the approach adopted was: the definition of the Mandelbrot set and its characteristics; the relationship between the Mandelbrot set and Julia set; how to find by using the Mandelbrot set. One of the tools used to help the teaching was Geogeobra, a dynamic software that allows the student to build the Mandelbrot set. Through this study, it is expected to motivate the learning of complex numbers by using fractal obtained by the study of function ( ) . Obtaining, as a result, a differentiated and motivating way of learning for a better understanding and intellectual development of the students.
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spelling Vieira, Ewerton Rochahttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4469919D9Vieira, Ewerton RochaLima, Lidiane dos Santos Monteiro deVasconcelos, José Eder Salvador dehttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4298130U5Reis, Márcio Vaiz dos2016-10-04T10:46:49Z2016-08-29REIS, Márcio Vaiz dos. Conjunto de Mandelbrot. 2016. 74 f. Dissertação ( Mestrado Profissional em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2016.http://repositorio.bc.ufg.br/tede/handle/tede/6343The purpose of this dissertation is to present an introductory approach to the complex dynamics and fractal geometry, especially the Mandelbrot set. With the goal to simplify and stimulate the introduction of complex number in high school, the approach adopted was: the definition of the Mandelbrot set and its characteristics; the relationship between the Mandelbrot set and Julia set; how to find by using the Mandelbrot set. One of the tools used to help the teaching was Geogeobra, a dynamic software that allows the student to build the Mandelbrot set. Through this study, it is expected to motivate the learning of complex numbers by using fractal obtained by the study of function ( ) . Obtaining, as a result, a differentiated and motivating way of learning for a better understanding and intellectual development of the students.Esse trabalho apresenta uma abordagem introdutória para a dinâmica complexa e a geometria fractal, em especial o conjunto de Mandelbrot. Com objetivo de facilitar e motivar a interação dos alunos com o ensino dos números complexos, a abordagem adotada foi: a definição do conjunto de Mandelbrot e suas características; a relação entre o conjunto de Mandelbrot e o conjunto de Julia; a relação do conjunto de Mandelbrot e o número . Uma das ferramentas utilizadas para auxiliar o professor foi o Geogeobra, um software dinâmico que permite o aluno a construção do conjunto de Mandelbrot. Por meio deste trabalho, espera-se motivar o ensino dos números complexos através do fractal obtido pelo estudo da função ( ) . Obtendo assim, como resultado, uma forma diferenciada e motivadora do aprendizado do aluno, garantindo um melhor entendimento e desenvolvimento intelectual.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/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/openAccessGeometria fractalConjunto de MandelbrotConjunto de Julia e GeogebraFractal geometryMandelbrot setJulia set and GeogebraCIENCIAS EXATAS E DA TERRA::MATEMATICAConjunto de MandelbrotMandelbrot setinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis4280721485626151024600600600600-4268777512335152015-70908234179844016942075167498588264571reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; 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dc.title.por.fl_str_mv Conjunto de Mandelbrot
dc.title.alternative.eng.fl_str_mv Mandelbrot set
title Conjunto de Mandelbrot
spellingShingle Conjunto de Mandelbrot
Reis, Márcio Vaiz dos
Geometria fractal
Conjunto de Mandelbrot
Conjunto de Julia e Geogebra
Fractal geometry
Mandelbrot set
Julia set and Geogebra
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Conjunto de Mandelbrot
title_full Conjunto de Mandelbrot
title_fullStr Conjunto de Mandelbrot
title_full_unstemmed Conjunto de Mandelbrot
title_sort Conjunto de Mandelbrot
author Reis, Márcio Vaiz dos
author_facet Reis, Márcio Vaiz dos
author_role author
dc.contributor.advisor1.fl_str_mv Vieira, Ewerton Rocha
dc.contributor.advisor1Lattes.fl_str_mv http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4469919D9
dc.contributor.referee1.fl_str_mv Vieira, Ewerton Rocha
dc.contributor.referee2.fl_str_mv Lima, Lidiane dos Santos Monteiro de
dc.contributor.referee3.fl_str_mv Vasconcelos, José Eder Salvador de
dc.contributor.authorLattes.fl_str_mv http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4298130U5
dc.contributor.author.fl_str_mv Reis, Márcio Vaiz dos
contributor_str_mv Vieira, Ewerton Rocha
Vieira, Ewerton Rocha
Lima, Lidiane dos Santos Monteiro de
Vasconcelos, José Eder Salvador de
dc.subject.por.fl_str_mv Geometria fractal
Conjunto de Mandelbrot
Conjunto de Julia e Geogebra
Fractal geometry
Mandelbrot set
Julia set and Geogebra
topic Geometria fractal
Conjunto de Mandelbrot
Conjunto de Julia e Geogebra
Fractal geometry
Mandelbrot set
Julia set and Geogebra
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description The purpose of this dissertation is to present an introductory approach to the complex dynamics and fractal geometry, especially the Mandelbrot set. With the goal to simplify and stimulate the introduction of complex number in high school, the approach adopted was: the definition of the Mandelbrot set and its characteristics; the relationship between the Mandelbrot set and Julia set; how to find by using the Mandelbrot set. One of the tools used to help the teaching was Geogeobra, a dynamic software that allows the student to build the Mandelbrot set. Through this study, it is expected to motivate the learning of complex numbers by using fractal obtained by the study of function ( ) . Obtaining, as a result, a differentiated and motivating way of learning for a better understanding and intellectual development of the students.
publishDate 2016
dc.date.accessioned.fl_str_mv 2016-10-04T10:46:49Z
dc.date.issued.fl_str_mv 2016-08-29
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, Márcio Vaiz dos. Conjunto de Mandelbrot. 2016. 74 f. Dissertação ( Mestrado Profissional em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2016.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/6343
identifier_str_mv REIS, Márcio Vaiz dos. Conjunto de Mandelbrot. 2016. 74 f. Dissertação ( Mestrado Profissional em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2016.
url http://repositorio.bc.ufg.br/tede/handle/tede/6343
dc.language.iso.fl_str_mv por
language por
dc.relation.program.fl_str_mv 4280721485626151024
dc.relation.confidence.fl_str_mv 600
600
600
600
dc.relation.department.fl_str_mv -4268777512335152015
dc.relation.cnpq.fl_str_mv -7090823417984401694
dc.relation.sponsorship.fl_str_mv 2075167498588264571
dc.rights.driver.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
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rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal de Goiás
dc.publisher.program.fl_str_mv PROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matemática (IME)
dc.publisher.initials.fl_str_mv UFG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Instituto de Matemática e Estatística - IME (RG)
publisher.none.fl_str_mv Universidade Federal de Goiás
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