Tipo
Artigos em Revista
Tipo de Documento
Artigo Completo
Título
Formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da Silva
Participantes na publicação
Ana Patrícia Martins (Author)
CIUHCT
Teresa Sousa (Author)
ESCOLA NAVAL
FACULDADE DE CIÊNCIAS E TECNOLOGIA DA UNIVERSIDADE NOVA DE LISBOA
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.
Data de Publicação
2022-07-10
Suporte
British Journal for the History of Mathematics
Identificadores da Publicação
ISSN - 2637-5451
Editora
Informa UK Limited
Número de Páginas
18
Página Inicial
212
Página Final
229
Identificadores do Documento
DOI -
https://doi.org/10.1080/26375451.2022.2082158
URL -
http://dx.doi.org/10.1080/26375451.2022.2082158
Identificadores de Qualidade
SCOPUS Q2 (2021) - 0.7 - History and Philosophy of Science
SCIMAGO Q3 (2021) - 204 - History and Philosophy of Science
Keywords
inclusion-exclusion principle
19th century
Daniel Augusto da Silva
Legendre
Sylvester
Poincaré