HISTORICAL ASPECTS OF THE DISCOVERY OF THE EULER CHARACTERISTIC AND SOME OF ITS DEVELOPMENTS IN MODERN TOPOLOGY

We begin by describing where and when Euler obtained the famous formula V + F = E + 2, which relates the number of vertices, edges and faces of a polyhedron that satisfies certain conditions. A few considerations are made about the relation of this formula with other problems and some difficulties o...

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Detalles Bibliográficos
Autor: Gonçalves, Daciberg Lima
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:Brasil
Institución:Sociedade Brasileira de História da Matemática (SBHMat)
Repositorio:Revista Brasileira de História da Matemática (Online)
Idioma:portugués
OAI Identifier:oai:ojs2.www.rbhm.org.br:article/170
Acceso en línea:http://www.rbhm.org.br/index.php/RBHM/article/view/170
Access Level:acceso abierto
Palabra clave:Euler characteristic
topology
characteristic classes
Descripción
Sumario:We begin by describing where and when Euler obtained the famous formula V + F = E + 2, which relates the number of vertices, edges and faces of a polyhedron that satisfies certain conditions. A few considerations are made about the relation of this formula with other problems and some difficulties of the original proof given by Euler. Then we move to the end of the 19th and beginning of the 20th century when the Euler  haracteristic and its generalization were linked to new topics in topology. Finally we present some of the generalizations of Euler characteristic which are used in recent (in the past 50 years) developments of topology.