Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números

The present thesis is an analysis of Adrien-Marie Legendre s works on Number Theory, with a certain emphasis on his 1830 edition of Theory of Numbers. The role played by these works in their historical context and their influence on the development of Number Theory was investigated. A biographic stu...

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1. Verfasser: Ramos, Maria Aparecida Roseane
Weitere Verfasser: Fossa, John Andrew
Format: doctoralThesis
Sprache:por
Veröffentlicht: Universidade Federal do Rio Grande do Norte
Schlagworte:
História da matemática
História da teoria dos números
Adrien-Marie Legendre
History of the mathematics
History of number theory
CNPQ::CIENCIAS HUMANAS::EDUCACAO
Online Zugang:https://repositorio.ufrn.br/jspui/handle/123456789/14306
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id ri-123456789-14306
record_format dspace
institution Repositório Institucional
collection RI - UFRN
language por
topic História da matemática
História da teoria dos números
Adrien-Marie Legendre
History of the mathematics
History of number theory
Adrien-Marie Legendre
CNPQ::CIENCIAS HUMANAS::EDUCACAO
spellingShingle História da matemática
História da teoria dos números
Adrien-Marie Legendre
History of the mathematics
History of number theory
Adrien-Marie Legendre
CNPQ::CIENCIAS HUMANAS::EDUCACAO
Ramos, Maria Aparecida Roseane
Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números
description The present thesis is an analysis of Adrien-Marie Legendre s works on Number Theory, with a certain emphasis on his 1830 edition of Theory of Numbers. The role played by these works in their historical context and their influence on the development of Number Theory was investigated. A biographic study of Legendre (1752-1833) was undertaken, in which both his personal relations and his scientific productions were related to certain historical elements of the development of both his homeland, France, and the sciences in general, during the 18th and 19th centuries This study revealed notable characteristics of his personality, as well as his attitudes toward his mathematical contemporaries, especially with regard to his seemingly incessant quarrels with Gauss about the priority of various of their scientific discoveries. This is followed by a systematic study of Lagrange s work on Number Theory, including a comparative reading of certain topics, especially that of his renowned law of quadratic reciprocity, with texts of some of his contemporaries. In this way, the dynamics of the evolution of his thought in relation to his semantics, the organization of his demonstrations and his number theoretical discoveries was delimited. Finally, the impact of Legendre s work on Number Theory on the French mathematical community of the time was investigated. This investigation revealed that he not only made substantial contributions to this branch of Mathematics, but also inspired other mathematicians to advance this science even further. This indeed is a fitting legacy for his Theory of Numbers, the first modern text on Higher Arithmetic, on which he labored half his life, producing various editions. Nevertheless, Legendre also received many posthumous honors, including having his name perpetuated on the Trocadéro face of the Eiffel Tower, which contains a list of 72 eminent scientists, and having a street and an alley in Paris named after him
author2 Fossa, John Andrew
author_facet Fossa, John Andrew
Ramos, Maria Aparecida Roseane
format doctoralThesis
author Ramos, Maria Aparecida Roseane
author_sort Ramos, Maria Aparecida Roseane
title Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números
title_short Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números
title_full Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números
title_fullStr Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números
title_full_unstemmed Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números
title_sort adrien-marie legendre (1752-1833) e suas obras em teoria dos números
publisher Universidade Federal do Rio Grande do Norte
publishDate 2014
url https://repositorio.ufrn.br/jspui/handle/123456789/14306
work_keys_str_mv AT ramosmariaaparecidaroseane adrienmarielegendre17521833esuasobrasemteoriadosnumeros
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spelling ri-123456789-143062017-11-01T16:52:07Z Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números Ramos, Maria Aparecida Roseane Fossa, John Andrew http://lattes.cnpq.br/2859541095732022 http://lattes.cnpq.br/2466525106349625 Sá, Pedro Franco de http://lattes.cnpq.br/4323922632919962 Sad, Ligia Arantes http://lattes.cnpq.br/1714140036102231 Mendes, Iran Abreu http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4704236U8 Sousa, Giselle Costa de http://lattes.cnpq.br/1300121866958282 História da matemática História da teoria dos números Adrien-Marie Legendre History of the mathematics History of number theory Adrien-Marie Legendre CNPQ::CIENCIAS HUMANAS::EDUCACAO The present thesis is an analysis of Adrien-Marie Legendre s works on Number Theory, with a certain emphasis on his 1830 edition of Theory of Numbers. The role played by these works in their historical context and their influence on the development of Number Theory was investigated. A biographic study of Legendre (1752-1833) was undertaken, in which both his personal relations and his scientific productions were related to certain historical elements of the development of both his homeland, France, and the sciences in general, during the 18th and 19th centuries This study revealed notable characteristics of his personality, as well as his attitudes toward his mathematical contemporaries, especially with regard to his seemingly incessant quarrels with Gauss about the priority of various of their scientific discoveries. This is followed by a systematic study of Lagrange s work on Number Theory, including a comparative reading of certain topics, especially that of his renowned law of quadratic reciprocity, with texts of some of his contemporaries. In this way, the dynamics of the evolution of his thought in relation to his semantics, the organization of his demonstrations and his number theoretical discoveries was delimited. Finally, the impact of Legendre s work on Number Theory on the French mathematical community of the time was investigated. This investigation revealed that he not only made substantial contributions to this branch of Mathematics, but also inspired other mathematicians to advance this science even further. This indeed is a fitting legacy for his Theory of Numbers, the first modern text on Higher Arithmetic, on which he labored half his life, producing various editions. Nevertheless, Legendre also received many posthumous honors, including having his name perpetuated on the Trocadéro face of the Eiffel Tower, which contains a list of 72 eminent scientists, and having a street and an alley in Paris named after him Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Este trabalho teve por objetivo inventariar, sistematizar e avaliar as obras em Teoria dos Números do matemático francês Adrien-Marie Legendre (1752-1833), com certa ênfase no seu livro Teoria dos Números, edição francesa de 1830, bem como realizar um estudo histórico da vida desse matemático. Para tanto, foi investigado o papel desempenhado por essas obras e sua influência no desenvolvimento da Teoria dos Números no contexto de sua época. Uma leitura da vida de Adrien-Marie Legendre foi realizada por meio de suas relações pessoais e de suas produções científicas e colocou em evidência certos elementos históricos do desenvolvimento de um povo, das ciências e suas possíveis consequências que nortearam a própria evolução da sociedade francesa dos séculos XVIII-XIX, e revelou características marcantes da personalidade de Legendre no meio matemático contemporâneo, como as infindáveis querelas com Gauss a respeito de prioridades de descobertas científicas. Um estudo sistemático da obra Teoria dos Números (1830) num contexto histórico-social e a análise de certos conteúdos da obra comparados a alguns textos de outros autores nos permitiram compreender a evolução dinâmica dos caminhos percorridos pelo autor, quanto à semântica, à organização das demonstrações, à estrutura lógico-dedutiva que permearam suas descobertas matemáticas em Teoria dos Números, a exemplo da sua famosa lei de reciprocidade. O impacto causado por suas obras em Teoria dos Números na comunidade matemática francesa da época e as contribuições do autor à ciência antes e depois da publicação da obra revelou que Teoria dos Números, obra à qual o autor consagrou mais da metade de sua vida no intuito de aperfeiçoá-la, tornou notória a honra que lhe é devida como o primeiro tratado de uma Aritmética superior que tanto inspirou a outros matemáticos para o avanço dessa ciência no século XX. Legendre recebeu homenagens póstumas dos matemáticos Beaumont, e Poisson, que inclusive discursou em seu funeral, e o seu nome se encontra perpetuado na face Trocadéro da Torre Eiffel que contém uma lista de 72 ilustres cientistas e dá nome a uma passagem e a uma rua do 17º bairro da cidade de Paris 2014-12-17T14:36:13Z 2011-02-16 2014-12-17T14:36:13Z 2010-12-14 doctoralThesis RAMOS, Maria Aparecida Roseane. Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números. 2010. 258 f. Tese (Doutorado em Educação) - Universidade Federal do Rio Grande do Norte, Natal, 2010. https://repositorio.ufrn.br/jspui/handle/123456789/14306 por Acesso Aberto application/pdf application/pdf Universidade Federal do Rio Grande do Norte BR UFRN Programa de Pós-Graduação em Educação Educação

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