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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| 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 |
| 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. |
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