Formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da Silva

Detalhes bibliográficos
Autor(a) principal: martins, ana patrícia
Data de Publicação: 2022
Outros Autores: Sousa, Teresa
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.19/7763
Resumo: The inclusion–exclusion principle is a simple, intuitive, and extremely versatile result. It is one of the most useful methods for counting and it can be used in different areas of mathematics. In the eighteenth century, the first uses of this result that appear in the literature are related to the study of problems of games of chance. However, the first formulations of this principle appear, independently by several authors, only in the nineteenth century. In this article, we study the formulations obtained by Adrien-Marie Legendre, Daniel Augusto da Silva, James Joseph Sylvester, and Henri Poincaré. We highlight the contribution of the Portuguese mathematician Daniel Augusto da Silva, since his formulation can be applied to different problems of number theory, whenever collections of numbers satisfying certain properties are involved, and this is the reason why his formulation stands out compared with all the others.
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spelling Formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da SilvaThe inclusion–exclusion principle is a simple, intuitive, and extremely versatile result. It is one of the most useful methods for counting and it can be used in different areas of mathematics. In the eighteenth century, the first uses of this result that appear in the literature are related to the study of problems of games of chance. However, the first formulations of this principle appear, independently by several authors, only in the nineteenth century. In this article, we study the formulations obtained by Adrien-Marie Legendre, Daniel Augusto da Silva, James Joseph Sylvester, and Henri Poincaré. We highlight the contribution of the Portuguese mathematician Daniel Augusto da Silva, since his formulation can be applied to different problems of number theory, whenever collections of numbers satisfying certain properties are involved, and this is the reason why his formulation stands out compared with all the others.Repositório Científico do Instituto Politécnico de Viseumartins, ana patríciaSousa, Teresa2023-04-19T14:36:42Z20222022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.19/7763eng10.1080/26375451.2022.2082158info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-04-22T02:31:11Zoai:repositorio.ipv.pt:10400.19/7763Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:50:04.429459Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da Silva
title Formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da Silva
spellingShingle Formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da Silva
martins, ana patrícia
title_short Formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da Silva
title_full Formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da Silva
title_fullStr Formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da Silva
title_full_unstemmed Formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da Silva
title_sort Formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da Silva
author martins, ana patrícia
author_facet martins, ana patrícia
Sousa, Teresa
author_role author
author2 Sousa, Teresa
author2_role author
dc.contributor.none.fl_str_mv Repositório Científico do Instituto Politécnico de Viseu
dc.contributor.author.fl_str_mv martins, ana patrícia
Sousa, Teresa
description The inclusion–exclusion principle is a simple, intuitive, and extremely versatile result. It is one of the most useful methods for counting and it can be used in different areas of mathematics. In the eighteenth century, the first uses of this result that appear in the literature are related to the study of problems of games of chance. However, the first formulations of this principle appear, independently by several authors, only in the nineteenth century. In this article, we study the formulations obtained by Adrien-Marie Legendre, Daniel Augusto da Silva, James Joseph Sylvester, and Henri Poincaré. We highlight the contribution of the Portuguese mathematician Daniel Augusto da Silva, since his formulation can be applied to different problems of number theory, whenever collections of numbers satisfying certain properties are involved, and this is the reason why his formulation stands out compared with all the others.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-01-01T00:00:00Z
2023-04-19T14:36:42Z
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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.19/7763
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