A simple proof of Abel’s theorem on the lemniscate
| dc.citation.epage | 49 | |
| dc.citation.issue | 12 | |
| dc.citation.journalAbbreviatedTitle | ing.cienc. | eng |
| dc.citation.journalTitle | Ingeniería y Ciencia | eng |
| dc.citation.spage | 43 | |
| dc.citation.volume | 6 | |
| dc.contributor.affiliation | Universidad del Tolima | spa |
| dc.contributor.author | Solanilla, Leonardo | spa |
| dc.contributor.author | Palacio, Óscar | spa |
| dc.contributor.author | Hernández, Uriel | spa |
| dc.coverage.spatial | Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees | eng |
| dc.date | 2010-12-01 | |
| dc.date.accessioned | 2019-11-22T19:01:23Z | |
| dc.date.available | 2019-11-22T19:01:23Z | |
| dc.date.issued | 2010-12-01 | |
| dc.description | Since Abel's original publication in 1827, his remarkable theorem on the constructibility of the division of the lemniscata has been demonstrated with the help of the theory of elliptic functions. The test given by Rosen in 1981 is considered, today, as definitive. It also uses the modern and intricate Class Field Theory. Here is a new, short and simple demonstration of Abel's theorem for the lemniscata along with its reciprocal. The only tools are the additive properties of the Gaussian lemniscological functions and some elements of Galois theory. | eng |
| dc.description | Desde la publicación original de Abel en 1827, su notable teorema sobre la constructibilidad de la división de la lemniscata se ha demostrado con ayuda de la teoría de las funciones elípticas. La prueba dada por Rosen en 1981 seconsidera, hoy por hoy, como definitiva. En ella se utiliza, además, la moderna e intrincada Class Field Theory. Aquí se presenta una demostración nueva, cortay simple del teorema de Abel para la lemniscata junto con su recíproco. Las únicas herramientas son las propiedades aditivas de las funciones lemniscáticas de Gauss y algunos elementos de teoría de Galois. | spa |
| dc.format | application/pdf | |
| dc.identifier.issn | 2256-4314 | |
| dc.identifier.issn | 1794-9165 | |
| dc.identifier.uri | http://hdl.handle.net/10784/14480 | |
| dc.language.iso | eng | eng |
| dc.publisher | Universidad EAFIT | spa |
| dc.relation.isversionof | http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/331 | |
| dc.relation.uri | http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/331 | |
| dc.rights | Copyright (c) 2010 Leonardo Solanilla, Óscar Palacio, Uriel Hernández | eng |
| dc.rights.accessrights | info:eu-repo/semantics/openAccess | eng |
| dc.rights.local | Acceso abierto | spa |
| dc.source | instname:Universidad EAFIT | |
| dc.source | reponame:Repositorio Institucional Universidad EAFIT | |
| dc.source | Ingeniería y Ciencia; Vol 6, No 12 (2010) | spa |
| dc.subject.keyword | Abel'S Theorem On The Lemniscata | eng |
| dc.subject.keyword | Gauss Lemniscratic Functions | eng |
| dc.subject.keyword | Geometric Constructions | eng |
| dc.subject.keyword | Teorema De Abel Sobre La Lemniscata | spa |
| dc.subject.keyword | Funciones Lemniscáticas De Gauss | spa |
| dc.subject.keyword | Construcciones Geométricas | spa |
| dc.title | A simple proof of Abel’s theorem on the lemniscate | eng |
| dc.title | Demostración simple del teorema de Abel sobre la lemniscata | spa |
| dc.type | article | eng |
| dc.type | info:eu-repo/semantics/article | eng |
| dc.type | publishedVersion | eng |
| dc.type | info:eu-repo/semantics/publishedVersion | eng |
| dc.type.local | Artículo | spa |