A simple proof of Abel’s theorem on the lemniscate
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 i...
- Autores:
-
Solanilla, Leonardo
Palacio, Óscar
Hernández, Uriel
- Tipo de recurso:
- Fecha de publicación:
- 2010
- Institución:
- Universidad EAFIT
- Repositorio:
- Repositorio EAFIT
- Idioma:
- eng
- OAI Identifier:
- oai:repository.eafit.edu.co:10784/14480
- Acceso en línea:
- http://hdl.handle.net/10784/14480
- Palabra clave:
- Abel'S Theorem On The Lemniscata
Gauss Lemniscratic Functions
Geometric Constructions
Teorema De Abel Sobre La Lemniscata
Funciones Lemniscáticas De Gauss
Construcciones Geométricas
- Rights
- License
- Copyright (c) 2010 Leonardo Solanilla, Óscar Palacio, Uriel Hernández
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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 degrees2010-12-012019-11-22T19:01:23Z2010-12-012019-11-22T19:01:23Z2256-43141794-9165http://hdl.handle.net/10784/14480Since 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.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.application/pdfengUniversidad EAFIThttp://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/331http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/331Copyright (c) 2010 Leonardo Solanilla, Óscar Palacio, Uriel HernándezAcceso abiertohttp://purl.org/coar/access_right/c_abf2instname:Universidad EAFITreponame:Repositorio Institucional Universidad EAFITIngeniería y Ciencia; Vol 6, No 12 (2010)A simple proof of Abel’s theorem on the lemniscateDemostración simple del teorema de Abel sobre la lemniscataarticleinfo:eu-repo/semantics/articlepublishedVersioninfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Abel'S Theorem On The LemniscataGauss Lemniscratic FunctionsGeometric ConstructionsTeorema De Abel Sobre La LemniscataFunciones Lemniscáticas De GaussConstrucciones GeométricasSolanilla, LeonardoPalacio, ÓscarHernández, UrielUniversidad del TolimaIngeniería y Ciencia6124349ing.cienc.THUMBNAILminaitura-ig_Mesa de trabajo 1.jpgminaitura-ig_Mesa de trabajo 1.jpgimage/jpeg265796https://repository.eafit.edu.co/bitstreams/afb55855-2449-421e-a538-cc9c8b346ea8/downloadda9b21a5c7e00c7f1127cef8e97035e0MD51ORIGINAL2.pdf2.pdfTexto completo PDFapplication/pdf149289https://repository.eafit.edu.co/bitstreams/b982ef5c-5388-4930-9ca3-6d7a037b3b5c/downloadcd2cbebd0f93c22f156d364049f14e56MD52articulo.htmlarticulo.htmlTexto completo HTMLtext/html373https://repository.eafit.edu.co/bitstreams/7d713c4f-f192-4558-98ef-cb62a906c1d7/download69f4bded8ac78c10d2ce8aad1c2740c2MD5310784/14480oai:repository.eafit.edu.co:10784/144802020-03-02 22:19:58.366open.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co |
| dc.title.eng.fl_str_mv |
A simple proof of Abel’s theorem on the lemniscate |
| dc.title.spa.fl_str_mv |
Demostración simple del teorema de Abel sobre la lemniscata |
| title |
A simple proof of Abel’s theorem on the lemniscate |
| spellingShingle |
A simple proof of Abel’s theorem on the lemniscate Abel'S Theorem On The Lemniscata Gauss Lemniscratic Functions Geometric Constructions Teorema De Abel Sobre La Lemniscata Funciones Lemniscáticas De Gauss Construcciones Geométricas |
| title_short |
A simple proof of Abel’s theorem on the lemniscate |
| title_full |
A simple proof of Abel’s theorem on the lemniscate |
| title_fullStr |
A simple proof of Abel’s theorem on the lemniscate |
| title_full_unstemmed |
A simple proof of Abel’s theorem on the lemniscate |
| title_sort |
A simple proof of Abel’s theorem on the lemniscate |
| dc.creator.fl_str_mv |
Solanilla, Leonardo Palacio, Óscar Hernández, Uriel |
| dc.contributor.author.spa.fl_str_mv |
Solanilla, Leonardo Palacio, Óscar Hernández, Uriel |
| dc.contributor.affiliation.spa.fl_str_mv |
Universidad del Tolima |
| dc.subject.keyword.eng.fl_str_mv |
Abel'S Theorem On The Lemniscata Gauss Lemniscratic Functions Geometric Constructions |
| topic |
Abel'S Theorem On The Lemniscata Gauss Lemniscratic Functions Geometric Constructions Teorema De Abel Sobre La Lemniscata Funciones Lemniscáticas De Gauss Construcciones Geométricas |
| dc.subject.keyword.spa.fl_str_mv |
Teorema De Abel Sobre La Lemniscata Funciones Lemniscáticas De Gauss Construcciones Geométricas |
| 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. |
| publishDate |
2010 |
| dc.date.issued.none.fl_str_mv |
2010-12-01 |
| dc.date.available.none.fl_str_mv |
2019-11-22T19:01:23Z |
| dc.date.accessioned.none.fl_str_mv |
2019-11-22T19:01:23Z |
| dc.date.none.fl_str_mv |
2010-12-01 |
| dc.type.eng.fl_str_mv |
article info:eu-repo/semantics/article publishedVersion info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
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Artículo |
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publishedVersion |
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2256-4314 1794-9165 |
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http://hdl.handle.net/10784/14480 |
| identifier_str_mv |
2256-4314 1794-9165 |
| url |
http://hdl.handle.net/10784/14480 |
| dc.language.iso.eng.fl_str_mv |
eng |
| language |
eng |
| dc.relation.isversionof.none.fl_str_mv |
http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/331 |
| dc.relation.uri.none.fl_str_mv |
http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/331 |
| dc.rights.eng.fl_str_mv |
Copyright (c) 2010 Leonardo Solanilla, Óscar Palacio, Uriel Hernández |
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http://purl.org/coar/access_right/c_abf2 |
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Acceso abierto |
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Copyright (c) 2010 Leonardo Solanilla, Óscar Palacio, Uriel Hernández Acceso abierto http://purl.org/coar/access_right/c_abf2 |
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application/pdf |
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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 |
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Universidad EAFIT |
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instname:Universidad EAFIT reponame:Repositorio Institucional Universidad EAFIT |
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Ingeniería y Ciencia; Vol 6, No 12 (2010) |
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