If You Were in My Shoes: Examples of Homogeneity in Geometry

Autores
Salvai, Marcos Luis
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
On which grounds are the elements of a set "all the same" in some sense? The reason may be in principle naive, based on (self-)perception or empathy, but for the sake of precision and to better organize ideas it may be convenient to resort to a transitive group of transformations.In this note we present three examples: a) Hidden symmetries of a distribution of planes. b) A distance compatible with homogeneity on the set of all ellipses, which may seem weird at first sight. c) A glimpse at Lie sphere geometry (admitting points as circles of radius zero in this framework).
Fil: Salvai, Marcos Luis. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Max Planck Institut Fuer Mathematik; Alemania
Materia
HOMOGENEITY
HEISENBERG GROUP
AFFINE-INVARIANT DISTANCE
LIE SPHERE GEOMETRY
STANDARD CONTACT STRUCTURE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/289876
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling If You Were in My Shoes: Examples of Homogeneity in GeometrySalvai, Marcos LuisHOMOGENEITYHEISENBERG GROUPAFFINE-INVARIANT DISTANCELIE SPHERE GEOMETRYSTANDARD CONTACT STRUCTUREhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1On which grounds are the elements of a set "all the same" in some sense? The reason may be in principle naive, based on (self-)perception or empathy, but for the sake of precision and to better organize ideas it may be convenient to resort to a transitive group of transformations.In this note we present three examples: a) Hidden symmetries of a distribution of planes. b) A distance compatible with homogeneity on the set of all ellipses, which may seem weird at first sight. c) A glimpse at Lie sphere geometry (admitting points as circles of radius zero in this framework).Fil: Salvai, Marcos Luis. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Max Planck Institut Fuer Mathematik; AlemaniaSpringer2025-05-29info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/289876Salvai, Marcos Luis; If You Were in My Shoes: Examples of Homogeneity in Geometry; Springer; Mathematical Intelligencer; 47; 4; 29-5-2025; 323-3260343-69931866-7414CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00283-025-10426-winfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00283-025-10426-winfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-08-25T15:06:14Zoai:ri.conicet.gov.ar:11336/289876instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982026-08-25 15:06:14.859CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv If You Were in My Shoes: Examples of Homogeneity in Geometry
title If You Were in My Shoes: Examples of Homogeneity in Geometry
spellingShingle If You Were in My Shoes: Examples of Homogeneity in Geometry
Salvai, Marcos Luis
HOMOGENEITY
HEISENBERG GROUP
AFFINE-INVARIANT DISTANCE
LIE SPHERE GEOMETRY
STANDARD CONTACT STRUCTURE
title_short If You Were in My Shoes: Examples of Homogeneity in Geometry
title_full If You Were in My Shoes: Examples of Homogeneity in Geometry
title_fullStr If You Were in My Shoes: Examples of Homogeneity in Geometry
title_full_unstemmed If You Were in My Shoes: Examples of Homogeneity in Geometry
title_sort If You Were in My Shoes: Examples of Homogeneity in Geometry
dc.creator.none.fl_str_mv Salvai, Marcos Luis
author Salvai, Marcos Luis
author_facet Salvai, Marcos Luis
author_role author
dc.subject.none.fl_str_mv HOMOGENEITY
HEISENBERG GROUP
AFFINE-INVARIANT DISTANCE
LIE SPHERE GEOMETRY
STANDARD CONTACT STRUCTURE
topic HOMOGENEITY
HEISENBERG GROUP
AFFINE-INVARIANT DISTANCE
LIE SPHERE GEOMETRY
STANDARD CONTACT STRUCTURE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv On which grounds are the elements of a set "all the same" in some sense? The reason may be in principle naive, based on (self-)perception or empathy, but for the sake of precision and to better organize ideas it may be convenient to resort to a transitive group of transformations.In this note we present three examples: a) Hidden symmetries of a distribution of planes. b) A distance compatible with homogeneity on the set of all ellipses, which may seem weird at first sight. c) A glimpse at Lie sphere geometry (admitting points as circles of radius zero in this framework).
Fil: Salvai, Marcos Luis. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Max Planck Institut Fuer Mathematik; Alemania
description On which grounds are the elements of a set "all the same" in some sense? The reason may be in principle naive, based on (self-)perception or empathy, but for the sake of precision and to better organize ideas it may be convenient to resort to a transitive group of transformations.In this note we present three examples: a) Hidden symmetries of a distribution of planes. b) A distance compatible with homogeneity on the set of all ellipses, which may seem weird at first sight. c) A glimpse at Lie sphere geometry (admitting points as circles of radius zero in this framework).
publishDate 2025
dc.date.none.fl_str_mv 2025-05-29
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/289876
Salvai, Marcos Luis; If You Were in My Shoes: Examples of Homogeneity in Geometry; Springer; Mathematical Intelligencer; 47; 4; 29-5-2025; 323-326
0343-6993
1866-7414
CONICET Digital
CONICET
url http://hdl.handle.net/11336/289876
identifier_str_mv Salvai, Marcos Luis; If You Were in My Shoes: Examples of Homogeneity in Geometry; Springer; Mathematical Intelligencer; 47; 4; 29-5-2025; 323-326
0343-6993
1866-7414
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00283-025-10426-w
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00283-025-10426-w
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.265058

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