Pub Date : 2021-08-17DOI: 10.47976/rbhm2020v20n4032-45
John A. Fossa
A proposiçao de que todo número perfeito é um número triangular era conhecida desde a antiguidade, pois foi conhecido por Jâmblico e, provavelmente, por Nicômacho. Depois de considerar os quatro tipos de perfeição dados por Jâmblico, apresenta-se as demonstrações de Jordanus, Bouvelles (demonstração por exemplificação) e Maurolico para a referida proposição. Todas elas supõem, no entanto, a recíproca do teorema IX.36 de Euclides, que só foi demonstrada, para números perfeitos pares, posteriormente por Euler.
{"title":"Sobre a Proposição de que Todo Número Perfeito é um Número Triangular","authors":"John A. Fossa","doi":"10.47976/rbhm2020v20n4032-45","DOIUrl":"https://doi.org/10.47976/rbhm2020v20n4032-45","url":null,"abstract":"A proposiçao de que todo número perfeito é um número triangular era conhecida desde a antiguidade, pois foi conhecido por Jâmblico e, provavelmente, por Nicômacho. Depois de considerar os quatro tipos de perfeição dados por Jâmblico, apresenta-se as demonstrações de Jordanus, Bouvelles (demonstração por exemplificação) e Maurolico para a referida proposição. Todas elas supõem, no entanto, a recíproca do teorema IX.36 de Euclides, que só foi demonstrada, para números perfeitos pares, posteriormente por Euler.","PeriodicalId":34320,"journal":{"name":"Revista Brasileira de Historia da Matematica","volume":"22 11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80135107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-17DOI: 10.47976/rbhm2020v20n4008-31
A. Calábria, S. Nobre
No dia 30 de março de 1999, nas dependências do Hotel Vitória Palace, em Vitória, Espírito Santo, foi fundada a Sociedade Brasileira de História da Matemática (SBHMat), na ocasião do III Seminário Nacional de História da Matemática. Evento esse, reunindo um grande número de pesquisadores brasileiros, na área de História da Matemática. Constando, também, com a distinta presença de alguns convidados estrangeiros. A decisão de se criar uma sociedade científica, específica em História da Matemática no Brasil, surgiu quando o grupo de pesquisadores, atuantes nesta área, constatou um crescimento significativo de trabalhos, envolvendo esse campo de pesquisa. No entanto, não havia um espaço que possibilitasse a divulgação e discussão desses trabalhos. Para veicular suas pesquisas, participavam de eventos ou congressos organizados por outras sociedades. O mesmo acontecia com relação às publicações. Na veemência de solucionar tal questão, esse grupo criou a SBHMat que, com seus direitos de sociedade, poderia organizar eventos e estabelecer um periódico específico em História da Matemática no Brasil. Nessa perspectiva, este texto tem por objetivo apresentar a história da criação da Sociedade Brasileira de História da Matemática e, não menos importante, concluir que, a partir da fundação da SBHMat, houve o fortalecimento da referida área no Brasil, podendo ser institucionalizada e considerada como campo de investigação científica, tanto em âmbito nacional quanto internacional.
{"title":"Sociedade Brasileira de História da Matemática. Uma história de sua criação e as contribuições ao desenvolvimento da área de pesquisa em História da Matemática no Brasil","authors":"A. Calábria, S. Nobre","doi":"10.47976/rbhm2020v20n4008-31","DOIUrl":"https://doi.org/10.47976/rbhm2020v20n4008-31","url":null,"abstract":"No dia 30 de março de 1999, nas dependências do Hotel Vitória Palace, em Vitória, Espírito Santo, foi fundada a Sociedade Brasileira de História da Matemática (SBHMat), na ocasião do III Seminário Nacional de História da Matemática. Evento esse, reunindo um grande número de pesquisadores brasileiros, na área de História da Matemática. Constando, também, com a distinta presença de alguns convidados estrangeiros. A decisão de se criar uma sociedade científica, específica em História da Matemática no Brasil, surgiu quando o grupo de pesquisadores, atuantes nesta área, constatou um crescimento significativo de trabalhos, envolvendo esse campo de pesquisa. No entanto, não havia um espaço que possibilitasse a divulgação e discussão desses trabalhos. Para veicular suas pesquisas, participavam de eventos ou congressos organizados por outras sociedades. O mesmo acontecia com relação às publicações. Na veemência de solucionar tal questão, esse grupo criou a SBHMat que, com seus direitos de sociedade, poderia organizar eventos e estabelecer um periódico específico em História da Matemática no Brasil. Nessa perspectiva, este texto tem por objetivo apresentar a história da criação da Sociedade Brasileira de História da Matemática e, não menos importante, concluir que, a partir da fundação da SBHMat, houve o fortalecimento da referida área no Brasil, podendo ser institucionalizada e considerada como campo de investigação científica, tanto em âmbito nacional quanto internacional.","PeriodicalId":34320,"journal":{"name":"Revista Brasileira de Historia da Matematica","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75615433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-22DOI: 10.47976/rbhm2018v18n351-22
Aline Germano Fonseca Coury, Denise Silva Vilela
For over twenty years, Frege tried to find the foundations of arithmetic through logic, and by doing this, he attempted to establish the truth and certainty of the knowledge. However, when he believed his work wasdone, Bertrand Russell sent him a letter pointing out a paradox, known as Russell‟s paradox. It is often considered that Russell identified the paradox in Frege‟s theories. However, as shown in this paper, Russell, Frege and also George Cantor contributedsignificantly to the identification of the paradox. In 1902, Russell encouraged Frege to reconsider a portion of his work based in a paradox built from Cantor‟s theories. Previously, in 1885, Cantor had warned Frege about taking extensions of concepts in the construction of his system. With these considerations, Frege managed to identify the precise law and definitions that allowed the generation of the paradox in his system. The objective of this paper is to present a historical reconstruction of the paradox in Frege‟s publications and discuss it considering the correspondences exchanged between him and Russell. We shall take special attention to the role played by each of these mathematicians in the identification of the paradox and its developments. We also will show how Frege anticipated the solutions and new theories that would arise when dealing with logico-mathematical paradoxes, including but not limited to Russell‟s paradox.
{"title":"Russell’s Paradox: a historical study about the paradox in Frege’s theories","authors":"Aline Germano Fonseca Coury, Denise Silva Vilela","doi":"10.47976/rbhm2018v18n351-22","DOIUrl":"https://doi.org/10.47976/rbhm2018v18n351-22","url":null,"abstract":"For over twenty years, Frege tried to find the foundations of arithmetic through logic, and by doing this, he attempted to establish the truth and certainty of the knowledge. However, when he believed his work wasdone, Bertrand Russell sent him a letter pointing out a paradox, known as Russell‟s paradox. It is often considered that Russell identified the paradox in Frege‟s theories. However, as shown in this paper, Russell, Frege and also George Cantor contributedsignificantly to the identification of the paradox. In 1902, Russell encouraged Frege to reconsider a portion of his work based in a paradox built from Cantor‟s theories. Previously, in 1885, Cantor had warned Frege about taking extensions of concepts in the construction of his system. With these considerations, Frege managed to identify the precise law and definitions that allowed the generation of the paradox in his system. The objective of this paper is to present a historical reconstruction of the paradox in Frege‟s publications and discuss it considering the correspondences exchanged between him and Russell. We shall take special attention to the role played by each of these mathematicians in the identification of the paradox and its developments. We also will show how Frege anticipated the solutions and new theories that would arise when dealing with logico-mathematical paradoxes, including but not limited to Russell‟s paradox.","PeriodicalId":34320,"journal":{"name":"Revista Brasileira de Historia da Matematica","volume":"166 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73136261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-16DOI: 10.47976/rbhm2019v19n3725-78
J. Dauben
The history of ancient Chinese mathematics and its applications has been greatly stimulated in the past few decades by remarkable archaeological discoveries of texts from the pre-Qin and later periods that make it possible to study in detail mathematical material from the time at which it was written. By examining the recent Warring States, Qin and Han bamboo mathematical texts currently being conserved and studied at Tsinghua University and Peking University in Beijing, the Yuelu Academy in Changsha, and the Hubei Museum in Wuhan, it is possible to shed new light on the history of early mathematical thought and its applications in ancient China. Also discussed here are developments of new techniques and justifications given for the problems that were a significant part of the growing mathematical corpus, and which eventually culminated in the comprehensive Nine Chapters on the Art of Mathematics. What follows is a revised text of an invited plenary lecture given during the 10th National Seminar on the History of Mathematics at UNICAMP in Campinas, SP, Brazil, on March 27, 2013.
{"title":"The Evolution of Mathematics in Ancient China: From the newly discovered 數 Shu and 算數書 Suan Shu Shu Bamboo Texts to the Nine Chapters on the Art of Mathematics","authors":"J. Dauben","doi":"10.47976/rbhm2019v19n3725-78","DOIUrl":"https://doi.org/10.47976/rbhm2019v19n3725-78","url":null,"abstract":"The history of ancient Chinese mathematics and its applications has been greatly stimulated in the past few decades by remarkable archaeological discoveries of texts from the pre-Qin and later periods that make it possible to study in detail mathematical material from the time at which it was written. By examining the recent Warring States, Qin and Han bamboo mathematical texts currently being conserved and studied at Tsinghua University and Peking University in Beijing, the Yuelu Academy in Changsha, and the Hubei Museum in Wuhan, it is possible to shed new light on the history of early mathematical thought and its applications in ancient China. Also discussed here are developments of new techniques and justifications given for the problems that were a significant part of the growing mathematical corpus, and which eventually culminated in the comprehensive Nine Chapters on the Art of Mathematics. What follows is a revised text of an invited plenary lecture given during the 10th National Seminar on the History of Mathematics at UNICAMP in Campinas, SP, Brazil, on March 27, 2013.","PeriodicalId":34320,"journal":{"name":"Revista Brasileira de Historia da Matematica","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77743085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-07DOI: 10.47976/RBHM2020V20N3913-33
M. Valente
The purpose of this work is to address the relation existing between ancient Greek (planar) practical geometry and ancient Greek (planar) pure geometry. In the first part of the work, we will consider practical and pure geometry and how pure geometry can be seen, in some respects, as arising from an idealization of practical geometry. From an analysis of relevant extant texts, we will make explicit the idealizations at play in pure geometry in relation to practical geometry, some of which are basically explicit in definitions, like that of segments (straight lines) in Euclid‘s Elements. Then, we will address how in pure geometry we, so tospeak, ―refer back‖ to practical geometry. This occurs in two ways. One, in the propositions of pure geometry (due to the accompanying figures). The other, when applying pure geometry. In this case, geometrical objects can represent practical figures like, e.g., a practical segment.
{"title":"From Practical to Pure Geometry and Back","authors":"M. Valente","doi":"10.47976/RBHM2020V20N3913-33","DOIUrl":"https://doi.org/10.47976/RBHM2020V20N3913-33","url":null,"abstract":"The purpose of this work is to address the relation existing between ancient Greek (planar) practical geometry and ancient Greek (planar) pure geometry. In the first part of the work, we will consider practical and pure geometry and how pure geometry can be seen, in some respects, as arising from an idealization of practical geometry. From an analysis of relevant extant texts, we will make explicit the idealizations at play in pure geometry in relation to practical geometry, some of which are basically explicit in definitions, like that of segments (straight lines) in Euclid‘s Elements. Then, we will address how in pure geometry we, so tospeak, ―refer back‖ to practical geometry. This occurs in two ways. One, in the propositions of pure geometry (due to the accompanying figures). The other, when applying pure geometry. In this case, geometrical objects can represent practical figures like, e.g., a practical segment.","PeriodicalId":34320,"journal":{"name":"Revista Brasileira de Historia da Matematica","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90166266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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