A raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?tica
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da UFRRJ |
Texto Completo: | https://tede.ufrrj.br/jspui/handle/jspui/5007 |
Resumo: | The central theme of this work is the use in the classroom of the interaction between Mathematics and Botany. The justification for choosing the subject is the undeniable presence of mathematical elements in Biology and the harmony resulting from their combination. To present and relate these two different areas, we will describe the concepts behind the irrational number, Fi (?), which is the result of a reason, called the Golden Ratio. First, we will bring the historical context in which the names of the main mathematicians, philosophers and thinkers are presented behind the projection of the Golden Reason. In this way, we will see that several mathematicians contributed to the evolution of concepts about the Golden Reason, without knowing that they did. Next, the theoretical constructions and bases for the observational field are described, which will be of great importance for the good development of classroom activities proposed here. Then their presence will be observed by means of images, which demonstrate with numbers the Golden Reason in their structures. The contextualization of the theme is proposed in a dynamic way inside and outside the classroom. We seek that this contextualization with natural elements, where man has not exerted influence in its forms and patterns, can contribute to the motivation of the students. We hope that the idea that studying mathematics is always to solve calculations on paper, without having a natural relation with the real world, is modified in the student's conception. Suggestions for activities will be presented with the objective of assisting the teacher during the approach of the contextualization between Golden Reason and Botany. However, several other activities can be developed within this theme. The application of some of these activities is part of this work, as well as a research with the students about the results obtained through this application. And so, while a lay observer can spend a lifetime without realizing the beauty and logical purpose behind various species in his garden - after reading this work, the reader will be introduced to a new way of looking at Mathematics. Concluding that contextualization is an indispensable element of student motivation, and that without this motivation, students can not visualize the mathematics around them and their concrete applications. |
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Forte, Vin?cius Leal do101.235.307-92http://lattes.cnpq.br/5246371559103159Forte, Vin?cius Leal doBarbosa, Aline MauricioVenceslau, Marilis Bahr Karam105.669.747-46http://lattes.cnpq.br/2646425780231381Silveira, Tiago Loyo2021-09-08T23:12:01Z2018-04-24SILVEIRA, Tiago Loyo. A raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?tica. 2018. 95 f. Disserta??o (Mestrado Profissional em Matem?tica em Rede Nacional) - Instituto de Ci?ncias Exatas, Universidade Federal Rural do Rio de Janeiro, Serop?dica - RJ, 2018.https://tede.ufrrj.br/jspui/handle/jspui/5007The central theme of this work is the use in the classroom of the interaction between Mathematics and Botany. The justification for choosing the subject is the undeniable presence of mathematical elements in Biology and the harmony resulting from their combination. To present and relate these two different areas, we will describe the concepts behind the irrational number, Fi (?), which is the result of a reason, called the Golden Ratio. First, we will bring the historical context in which the names of the main mathematicians, philosophers and thinkers are presented behind the projection of the Golden Reason. In this way, we will see that several mathematicians contributed to the evolution of concepts about the Golden Reason, without knowing that they did. Next, the theoretical constructions and bases for the observational field are described, which will be of great importance for the good development of classroom activities proposed here. Then their presence will be observed by means of images, which demonstrate with numbers the Golden Reason in their structures. The contextualization of the theme is proposed in a dynamic way inside and outside the classroom. We seek that this contextualization with natural elements, where man has not exerted influence in its forms and patterns, can contribute to the motivation of the students. We hope that the idea that studying mathematics is always to solve calculations on paper, without having a natural relation with the real world, is modified in the student's conception. Suggestions for activities will be presented with the objective of assisting the teacher during the approach of the contextualization between Golden Reason and Botany. However, several other activities can be developed within this theme. The application of some of these activities is part of this work, as well as a research with the students about the results obtained through this application. And so, while a lay observer can spend a lifetime without realizing the beauty and logical purpose behind various species in his garden - after reading this work, the reader will be introduced to a new way of looking at Mathematics. Concluding that contextualization is an indispensable element of student motivation, and that without this motivation, students can not visualize the mathematics around them and their concrete applications.A tem?tica central desse trabalho ? o uso em sala de aula da intera??o entre a Matem?tica e a Bot?nica. A justificativa para a escolha da tem?tica abordada ? a presen?a ineg?vel de elementos matem?ticos na Biologia e a harmonia resultante da combina??o destes. Para apresentar e relacionar essas duas diferentes ?reas, iremos descrever os conceitos por tr?s do n?mero irracional, Fi (?), que ? resultado de uma raz?o, denominada Raz?o ?urea. Primeiramente, traremos o contexto hist?rico, no qual s?o apresentados os nomes dos principais matem?ticos, fil?sofos e pensadores por tr?s da proje??o da Raz?o ?urea. Nesse caminho, veremos que diversos matem?ticos contribu?ram para a evolu??o dos conceitos sobre a Raz?o ?urea, sem saber que o faziam. Em seguida s?o descritas as constru??es e bases te?ricas para o campo observacional, que ser? de grande import?ncia para o bom desenvolvimento das atividades de sala de aula, aqui propostas. Ent?o, sua presen?a ser? observada por meio de imagens, que demonstram com os n?meros a Raz?o ?urea em suas estruturas. A contextualiza??o do tema ? proposta de uma forma din?mica dentro e fora da sala de aula. Buscamos que essa contextualiza??o com elementos naturais, onde o homem n?o exerceu influ?ncia em suas formas e padr?es, possa contribuir para a motiva??o dos alunos. Esperamos que a ideia de que estudar Matem?tica ? sempre resolver c?lculos no papel, sem que essa tenha uma rela??o natural com o mundo real, seja modificada na concep??o do aluno. Sugest?es de atividades ser?o apresentadas com o objetivo de auxiliar o professor durante a abordagem da contextualiza??o entre Raz?o ?urea e a Bot?nica. Por?m, diversas outras atividades podem ser desenvolvidas dentro desse tema. A aplica??o de algumas dessas atividades faz parte desse trabalho, bem como uma pesquisa com os alunos sobre os resultados obtidos atrav?s dessa aplica??o. E assim, embora um observador leigo possa passar toda uma vida sem perceber a beleza e o prop?sito l?gico por tr?s de v?rias esp?cies em seu jardim - ap?s a leitura deste trabalho, o leitor ser? apresentado a uma nova forma de encarar a Matem?tica. Concluindo que a contextualiza??o ? um elemento indispens?vel a motiva??o do aluno, e que sem essa motiva??o, o aluno n?o consegue visualizar a matem?tica ao seu redor e suas aplica??es concretas.Submitted by Sandra Pereira (srpereira@ufrrj.br) on 2021-09-08T23:12:01Z No. of bitstreams: 1 2018 - Tiago Loyo Silveira.pdf: 13795071 bytes, checksum: 33e0bec74b7d80a9b02507ba92eaf683 (MD5)Made available in DSpace on 2021-09-08T23:12:01Z (GMT). No. of bitstreams: 1 2018 - Tiago Loyo Silveira.pdf: 13795071 bytes, checksum: 33e0bec74b7d80a9b02507ba92eaf683 (MD5) Previous issue date: 2018-04-24application/pdfhttps://tede.ufrrj.br/retrieve/66609/2018%20-%20Tiago%20Loyo%20Silveira.pdf.jpgporUniversidade Federal Rural do Rio de JaneiroPrograma de P?s-Gradua??o em Matem?tica em Rede NacionalUFRRJBrasilInstituto de Ci?ncias ExatasBIEMBENGUT, Maria Salett. N?mero de Ouro e Se??o ?urea, Considera??es e Sugest?es para a Sala de Aula. Blumenau ? SC: Ed. da FURB, 1996. BERTATO, Fabio Maia. ?De Divina Proportione? ? de Luca Pacioli ? (Tradu??o anotada e comentada). Doutorado em Filosofia ? Universidade Estadual de Campinas - Instituto de Filosofia e Ci?ncias Humanas, 2008. Dispon?vel em: <http://www.scribd.com/doc/18161028/De-Divina-Proportione-de-Luca-Pacioli-Traducao- Anotada-e-Comentada->. Acesso em: 04 mar?o 2018. BONELL, Carmen. La divina proporci?n. Las formas geom?tricas. Barcelona ? Espanha: Edicions UPC, 1999. BOYER, Carl B. Hist?ria da Matem?tica/Carl B. Boyer, revista por Uta C. Merzbach; tradu??o Elza F. Gomide ? 2.ed. S?o Paulo: Edgard Bl?cler, 1996. BRASIL. PCN: Orienta??es Educacionais Complementares aos Par?metros Curriculares Nacionais. Bras?lia: MEC, 2002. Dispon?vel em: <http://portal.mec.gov.br/component/tags/tag/33038>. Acesso em: 29 mar?o 2018. CARVALHO, Jurandir Jacques de. Raz?o ?urea. Monografia (curso de especializa??o para professores do ensino fundamental e m?dio) ? Universidade Federal de Minas Gerais, 2008. Dispon?vel em: < https://docgo.net/philosophy-of-money.html?utm_source=monografiarazao- aurea >. Acesso em: 04 mar?o 2018. CLEMENTE, Isaac. Geometria Fractal. Dispon?vel em: < https://www.infoescola.com/matematica/geometria-fractal/>. Acesso em: 28 mar?o 2018. COLE, K. C.. O Universo e a X?cara de Ch?. S?o Paulo ? SP: Ed. Record, 2006. EUCLIDES. Os Elementos/Euclides. Tradu??o e introdu??o de Irineu Bicudo. S?o Paulo ? SP: Ed. UNESP, 2009. FERRI, Mario Guimar?es. Bot?nica, Morfologia Externa das Plantas. S?o Paulo ? SP: Ed. Nobel, 2006. GAZAL?, Midhat J. Gnomon: from pharaohs to fractals. Princeton, New Jersey - EUA: Princeton University Press, 1999. HEMENWAY, Priya. O C?digo Secreto, A f?mula misteriosa que governa a arte, a natureza e a ci?ncia. EUA: Ed. Evergreen, 2005. HUNTLEY, H. E.. A Divina Propor??o, Um Ensaio sobre a Beleza na Matem?tica. Nova Iorque ? EUA. Trad. de Lu?s Carlos Asc?ncio Nunes. Bras?lia: Ed. Universidade de Bras?lia, 1985. JEAN, Roger V.. Mathematical Approach to Pattern and Form in Plant Growth. EUA: Ed. John Wiley & Sons, 1984. 93 L?VIO, Mario. Raz?o ?urea. A hist?ria de FI, um n?mero surpreendente. Rio de Janeiro/S?o Paulo: Ed. Record, 2009. PISANO, Leonardo (Leonardo Fibonacci). Liber Abaci ? Vers?o Resumida ? 1228. Dispon?vel em: < http://jnsilva.ludicum.org/hm2008_9/LiberAbaci.pdf>. Acesso em: 04 mar?o 2018 POSAMENTIER, Alfred S. & LEHMANN, Ingmar. The Fabulous Fibonacci Numbers. Nova Iorque ? EUA: Ed. Prometheus Books, 2007. TAPIA, Jes?s Alonso & FITA, Enrique Caturla. A Motiva??o em Sala de Aula - o que ?, e como se faz. 11. Ed ? S?o Paulo: Ed. Loyola, 2015. WEISSTEIN, Eric W. Logarithmic Spiral. MathWorld - A Wolfram. Dispon?vel em: <http://mathworld.wolfram.com/LogarithmicSpiral.html>. Acesso em: 04 mar?o 2018. ZAHN, Maur?cio. Sequ?ncia de Fibonacci e o N?mero de Ouro. Bag? ? RS: Ed. Ci?ncia Moderna, 2011.Raz?o ?ureaFibonacciFilotaxiaContextualiza??oGolden RatioFibonacciPhyllotaxisContextualizationMatem?ticaA raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?ticaThe golden ratio in botany - contextualized practices used as element of motivation in mathematics educationinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UFRRJinstname:Universidade Federal Rural do Rio de Janeiro (UFRRJ)instacron:UFRRJTHUMBNAIL2018 - Tiago Loyo Silveira.pdf.jpg2018 - Tiago Loyo Silveira.pdf.jpgimage/jpeg4157http://localhost:8080/tede/bitstream/jspui/5007/4/2018+-+Tiago+Loyo+Silveira.pdf.jpge2c8509ddf000807089b738e0e6b0566MD54TEXT2018 - Tiago Loyo Silveira.pdf.txt2018 - Tiago Loyo Silveira.pdf.txttext/plain134820http://localhost:8080/tede/bitstream/jspui/5007/3/2018+-+Tiago+Loyo+Silveira.pdf.txt0f70d5fdc85d17678b0d73e62d177037MD53ORIGINAL2018 - Tiago Loyo Silveira.pdf2018 - Tiago Loyo Silveira.pdfapplication/pdf2286285http://localhost:8080/tede/bitstream/jspui/5007/5/2018+-+Tiago+Loyo+Silveira.pdfbcda4b7a7df5b760c4663c3ee6bae8ecMD55LICENSElicense.txtlicense.txttext/plain; charset=utf-82165http://localhost:8080/tede/bitstream/jspui/5007/1/license.txtbd3efa91386c1718a7f26a329fdcb468MD51jspui/50072022-10-18 18:25:05.027oai:localhost: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Biblioteca Digital de Teses e Dissertaçõeshttps://tede.ufrrj.br/PUBhttps://tede.ufrrj.br/oai/requestbibliot@ufrrj.br||bibliot@ufrrj.bropendoar:2022-10-18T20:25:05Biblioteca Digital de Teses e Dissertações da UFRRJ - Universidade Federal Rural do Rio de Janeiro (UFRRJ)false |
dc.title.por.fl_str_mv |
A raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?tica |
dc.title.alternative.eng.fl_str_mv |
The golden ratio in botany - contextualized practices used as element of motivation in mathematics education |
title |
A raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?tica |
spellingShingle |
A raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?tica Silveira, Tiago Loyo Raz?o ?urea Fibonacci Filotaxia Contextualiza??o Golden Ratio Fibonacci Phyllotaxis Contextualization Matem?tica |
title_short |
A raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?tica |
title_full |
A raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?tica |
title_fullStr |
A raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?tica |
title_full_unstemmed |
A raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?tica |
title_sort |
A raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?tica |
author |
Silveira, Tiago Loyo |
author_facet |
Silveira, Tiago Loyo |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Forte, Vin?cius Leal do |
dc.contributor.advisor1ID.fl_str_mv |
101.235.307-92 |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/5246371559103159 |
dc.contributor.referee1.fl_str_mv |
Forte, Vin?cius Leal do |
dc.contributor.referee2.fl_str_mv |
Barbosa, Aline Mauricio |
dc.contributor.referee3.fl_str_mv |
Venceslau, Marilis Bahr Karam |
dc.contributor.authorID.fl_str_mv |
105.669.747-46 |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/2646425780231381 |
dc.contributor.author.fl_str_mv |
Silveira, Tiago Loyo |
contributor_str_mv |
Forte, Vin?cius Leal do Forte, Vin?cius Leal do Barbosa, Aline Mauricio Venceslau, Marilis Bahr Karam |
dc.subject.por.fl_str_mv |
Raz?o ?urea Fibonacci Filotaxia Contextualiza??o |
topic |
Raz?o ?urea Fibonacci Filotaxia Contextualiza??o Golden Ratio Fibonacci Phyllotaxis Contextualization Matem?tica |
dc.subject.eng.fl_str_mv |
Golden Ratio Fibonacci Phyllotaxis Contextualization |
dc.subject.cnpq.fl_str_mv |
Matem?tica |
description |
The central theme of this work is the use in the classroom of the interaction between Mathematics and Botany. The justification for choosing the subject is the undeniable presence of mathematical elements in Biology and the harmony resulting from their combination. To present and relate these two different areas, we will describe the concepts behind the irrational number, Fi (?), which is the result of a reason, called the Golden Ratio. First, we will bring the historical context in which the names of the main mathematicians, philosophers and thinkers are presented behind the projection of the Golden Reason. In this way, we will see that several mathematicians contributed to the evolution of concepts about the Golden Reason, without knowing that they did. Next, the theoretical constructions and bases for the observational field are described, which will be of great importance for the good development of classroom activities proposed here. Then their presence will be observed by means of images, which demonstrate with numbers the Golden Reason in their structures. The contextualization of the theme is proposed in a dynamic way inside and outside the classroom. We seek that this contextualization with natural elements, where man has not exerted influence in its forms and patterns, can contribute to the motivation of the students. We hope that the idea that studying mathematics is always to solve calculations on paper, without having a natural relation with the real world, is modified in the student's conception. Suggestions for activities will be presented with the objective of assisting the teacher during the approach of the contextualization between Golden Reason and Botany. However, several other activities can be developed within this theme. The application of some of these activities is part of this work, as well as a research with the students about the results obtained through this application. And so, while a lay observer can spend a lifetime without realizing the beauty and logical purpose behind various species in his garden - after reading this work, the reader will be introduced to a new way of looking at Mathematics. Concluding that contextualization is an indispensable element of student motivation, and that without this motivation, students can not visualize the mathematics around them and their concrete applications. |
publishDate |
2018 |
dc.date.issued.fl_str_mv |
2018-04-24 |
dc.date.accessioned.fl_str_mv |
2021-09-08T23:12:01Z |
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 |
SILVEIRA, Tiago Loyo. A raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?tica. 2018. 95 f. Disserta??o (Mestrado Profissional em Matem?tica em Rede Nacional) - Instituto de Ci?ncias Exatas, Universidade Federal Rural do Rio de Janeiro, Serop?dica - RJ, 2018. |
dc.identifier.uri.fl_str_mv |
https://tede.ufrrj.br/jspui/handle/jspui/5007 |
identifier_str_mv |
SILVEIRA, Tiago Loyo. A raz?o ?urea na bot?nica ? pr?ticas contextualizadas utilizadas como elemento de motiva??o da educa??o matem?tica. 2018. 95 f. Disserta??o (Mestrado Profissional em Matem?tica em Rede Nacional) - Instituto de Ci?ncias Exatas, Universidade Federal Rural do Rio de Janeiro, Serop?dica - RJ, 2018. |
url |
https://tede.ufrrj.br/jspui/handle/jspui/5007 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.references.por.fl_str_mv |
BIEMBENGUT, Maria Salett. N?mero de Ouro e Se??o ?urea, Considera??es e Sugest?es para a Sala de Aula. Blumenau ? SC: Ed. da FURB, 1996. BERTATO, Fabio Maia. ?De Divina Proportione? ? de Luca Pacioli ? (Tradu??o anotada e comentada). Doutorado em Filosofia ? Universidade Estadual de Campinas - Instituto de Filosofia e Ci?ncias Humanas, 2008. Dispon?vel em: <http://www.scribd.com/doc/18161028/De-Divina-Proportione-de-Luca-Pacioli-Traducao- Anotada-e-Comentada->. Acesso em: 04 mar?o 2018. BONELL, Carmen. La divina proporci?n. Las formas geom?tricas. Barcelona ? Espanha: Edicions UPC, 1999. BOYER, Carl B. Hist?ria da Matem?tica/Carl B. Boyer, revista por Uta C. Merzbach; tradu??o Elza F. Gomide ? 2.ed. S?o Paulo: Edgard Bl?cler, 1996. BRASIL. PCN: Orienta??es Educacionais Complementares aos Par?metros Curriculares Nacionais. Bras?lia: MEC, 2002. Dispon?vel em: <http://portal.mec.gov.br/component/tags/tag/33038>. Acesso em: 29 mar?o 2018. CARVALHO, Jurandir Jacques de. Raz?o ?urea. Monografia (curso de especializa??o para professores do ensino fundamental e m?dio) ? Universidade Federal de Minas Gerais, 2008. Dispon?vel em: < https://docgo.net/philosophy-of-money.html?utm_source=monografiarazao- aurea >. Acesso em: 04 mar?o 2018. CLEMENTE, Isaac. Geometria Fractal. Dispon?vel em: < https://www.infoescola.com/matematica/geometria-fractal/>. Acesso em: 28 mar?o 2018. COLE, K. C.. O Universo e a X?cara de Ch?. S?o Paulo ? SP: Ed. Record, 2006. EUCLIDES. Os Elementos/Euclides. Tradu??o e introdu??o de Irineu Bicudo. S?o Paulo ? SP: Ed. UNESP, 2009. FERRI, Mario Guimar?es. Bot?nica, Morfologia Externa das Plantas. S?o Paulo ? SP: Ed. Nobel, 2006. GAZAL?, Midhat J. Gnomon: from pharaohs to fractals. Princeton, New Jersey - EUA: Princeton University Press, 1999. HEMENWAY, Priya. O C?digo Secreto, A f?mula misteriosa que governa a arte, a natureza e a ci?ncia. EUA: Ed. Evergreen, 2005. HUNTLEY, H. E.. A Divina Propor??o, Um Ensaio sobre a Beleza na Matem?tica. Nova Iorque ? EUA. Trad. de Lu?s Carlos Asc?ncio Nunes. Bras?lia: Ed. Universidade de Bras?lia, 1985. JEAN, Roger V.. Mathematical Approach to Pattern and Form in Plant Growth. EUA: Ed. John Wiley & Sons, 1984. 93 L?VIO, Mario. Raz?o ?urea. A hist?ria de FI, um n?mero surpreendente. Rio de Janeiro/S?o Paulo: Ed. Record, 2009. PISANO, Leonardo (Leonardo Fibonacci). Liber Abaci ? Vers?o Resumida ? 1228. Dispon?vel em: < http://jnsilva.ludicum.org/hm2008_9/LiberAbaci.pdf>. Acesso em: 04 mar?o 2018 POSAMENTIER, Alfred S. & LEHMANN, Ingmar. The Fabulous Fibonacci Numbers. Nova Iorque ? EUA: Ed. Prometheus Books, 2007. TAPIA, Jes?s Alonso & FITA, Enrique Caturla. A Motiva??o em Sala de Aula - o que ?, e como se faz. 11. Ed ? S?o Paulo: Ed. Loyola, 2015. WEISSTEIN, Eric W. Logarithmic Spiral. MathWorld - A Wolfram. Dispon?vel em: <http://mathworld.wolfram.com/LogarithmicSpiral.html>. Acesso em: 04 mar?o 2018. ZAHN, Maur?cio. Sequ?ncia de Fibonacci e o N?mero de Ouro. Bag? ? RS: Ed. Ci?ncia Moderna, 2011. |
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