An elementary proof of Euler's formula using Cauchy's method

Detalhes bibliográficos
Autor(a) principal: Brasselet, Jean-Paul
Data de Publicação: 2021
Outros Autores: Thủy, Nguyn̂̃n Thị Bích [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.topol.2020.107558
http://hdl.handle.net/11449/205712
Resumo: The use of Cauchy's method to prove Euler's well-known formula is an object of many controversies. The purpose of this paper is to prove that Cauchy's method applies for convex polyhedra and not only for them, but also for surfaces such as the torus, the projective plane, the Klein bottle and the pinched torus.
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spelling An elementary proof of Euler's formula using Cauchy's methodCauchyDescartesEuler formulaPolyhedronThe use of Cauchy's method to prove Euler's well-known formula is an object of many controversies. The purpose of this paper is to prove that Cauchy's method applies for convex polyhedra and not only for them, but also for surfaces such as the torus, the projective plane, the Klein bottle and the pinched torus.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNRS I2M Aix-Marseille UniversitéUNESP Universidade Estadual Paulista “Júlio de Mesquita Filho”UNESP Universidade Estadual Paulista “Júlio de Mesquita Filho”FAPESP: 2015/06697-9Aix-Marseille UniversitéUniversidade Estadual Paulista (Unesp)Brasselet, Jean-PaulThủy, Nguyn̂̃n Thị Bích [UNESP]2021-06-25T10:19:59Z2021-06-25T10:19:59Z2021-04-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.topol.2020.107558Topology and its Applications, v. 293.0166-8641http://hdl.handle.net/11449/20571210.1016/j.topol.2020.1075582-s2.0-85099170323Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengTopology and its Applicationsinfo:eu-repo/semantics/openAccess2021-10-22T14:02:46Zoai:repositorio.unesp.br:11449/205712Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:46:31.554361Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv An elementary proof of Euler's formula using Cauchy's method
title An elementary proof of Euler's formula using Cauchy's method
spellingShingle An elementary proof of Euler's formula using Cauchy's method
Brasselet, Jean-Paul
Cauchy
Descartes
Euler formula
Polyhedron
title_short An elementary proof of Euler's formula using Cauchy's method
title_full An elementary proof of Euler's formula using Cauchy's method
title_fullStr An elementary proof of Euler's formula using Cauchy's method
title_full_unstemmed An elementary proof of Euler's formula using Cauchy's method
title_sort An elementary proof of Euler's formula using Cauchy's method
author Brasselet, Jean-Paul
author_facet Brasselet, Jean-Paul
Thủy, Nguyn̂̃n Thị Bích [UNESP]
author_role author
author2 Thủy, Nguyn̂̃n Thị Bích [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Aix-Marseille Université
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Brasselet, Jean-Paul
Thủy, Nguyn̂̃n Thị Bích [UNESP]
dc.subject.por.fl_str_mv Cauchy
Descartes
Euler formula
Polyhedron
topic Cauchy
Descartes
Euler formula
Polyhedron
description The use of Cauchy's method to prove Euler's well-known formula is an object of many controversies. The purpose of this paper is to prove that Cauchy's method applies for convex polyhedra and not only for them, but also for surfaces such as the torus, the projective plane, the Klein bottle and the pinched torus.
publishDate 2021
dc.date.none.fl_str_mv 2021-06-25T10:19:59Z
2021-06-25T10:19:59Z
2021-04-15
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/j.topol.2020.107558
Topology and its Applications, v. 293.
0166-8641
http://hdl.handle.net/11449/205712
10.1016/j.topol.2020.107558
2-s2.0-85099170323
url http://dx.doi.org/10.1016/j.topol.2020.107558
http://hdl.handle.net/11449/205712
identifier_str_mv Topology and its Applications, v. 293.
0166-8641
10.1016/j.topol.2020.107558
2-s2.0-85099170323
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Topology and its Applications
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808128559691071488

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