A new class of monohedral pentagonal spherical tilingswith GeoGebra
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/22148 |
Resumo: | By a monohedral spherical tiling we mean a decomposition of the sphereby geodesic congruent polygons. Here, making use of GeoGebra, a well known freeinteractive mathematics software, we show how to generate new classes of monohedralnon-convex triangular and new non-convex pentagonal spherical tilings, changing theside gluing rules of the regular spherical tetrahedral tiling, by means of a local actionof particular subgroups of spherical isometries. In both cases each face haspas areameasure.In relation to the new class of pentagonal tilings, we describe some of their propertiesand show the existence, in a special case, of an associated dihedral triangular spherical til-ing, that is, a tiling composed by two sets of congruent triangles.These classes of spherical tilings have emerged as a result of an interative constructionprocess, only possible by the use of newly produced GeoGebra tools and the dynamic inter-action capabilities of this software. |
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A new class of monohedral pentagonal spherical tilingswith GeoGebraSpherical geometryGeoGebraSpherical tilingsBy a monohedral spherical tiling we mean a decomposition of the sphereby geodesic congruent polygons. Here, making use of GeoGebra, a well known freeinteractive mathematics software, we show how to generate new classes of monohedralnon-convex triangular and new non-convex pentagonal spherical tilings, changing theside gluing rules of the regular spherical tetrahedral tiling, by means of a local actionof particular subgroups of spherical isometries. In both cases each face haspas areameasure.In relation to the new class of pentagonal tilings, we describe some of their propertiesand show the existence, in a special case, of an associated dihedral triangular spherical til-ing, that is, a tiling composed by two sets of congruent triangles.These classes of spherical tilings have emerged as a result of an interative constructionprocess, only possible by the use of newly produced GeoGebra tools and the dynamic inter-action capabilities of this software.European Mathematical Society2018-02-12T15:54:10Z2018-02-01T00:00:00Z2018-02info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/22148eng0032-515510.4171/PM/2006Breda, AnaSantos, José M. Santos dosinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:43:28Zoai:ria.ua.pt:10773/22148Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:56:23.236933Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
A new class of monohedral pentagonal spherical tilingswith GeoGebra |
title |
A new class of monohedral pentagonal spherical tilingswith GeoGebra |
spellingShingle |
A new class of monohedral pentagonal spherical tilingswith GeoGebra Breda, Ana Spherical geometry GeoGebra Spherical tilings |
title_short |
A new class of monohedral pentagonal spherical tilingswith GeoGebra |
title_full |
A new class of monohedral pentagonal spherical tilingswith GeoGebra |
title_fullStr |
A new class of monohedral pentagonal spherical tilingswith GeoGebra |
title_full_unstemmed |
A new class of monohedral pentagonal spherical tilingswith GeoGebra |
title_sort |
A new class of monohedral pentagonal spherical tilingswith GeoGebra |
author |
Breda, Ana |
author_facet |
Breda, Ana Santos, José M. Santos dos |
author_role |
author |
author2 |
Santos, José M. Santos dos |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Breda, Ana Santos, José M. Santos dos |
dc.subject.por.fl_str_mv |
Spherical geometry GeoGebra Spherical tilings |
topic |
Spherical geometry GeoGebra Spherical tilings |
description |
By a monohedral spherical tiling we mean a decomposition of the sphereby geodesic congruent polygons. Here, making use of GeoGebra, a well known freeinteractive mathematics software, we show how to generate new classes of monohedralnon-convex triangular and new non-convex pentagonal spherical tilings, changing theside gluing rules of the regular spherical tetrahedral tiling, by means of a local actionof particular subgroups of spherical isometries. In both cases each face haspas areameasure.In relation to the new class of pentagonal tilings, we describe some of their propertiesand show the existence, in a special case, of an associated dihedral triangular spherical til-ing, that is, a tiling composed by two sets of congruent triangles.These classes of spherical tilings have emerged as a result of an interative constructionprocess, only possible by the use of newly produced GeoGebra tools and the dynamic inter-action capabilities of this software. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-02-12T15:54:10Z 2018-02-01T00:00:00Z 2018-02 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/22148 |
url |
http://hdl.handle.net/10773/22148 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0032-5155 10.4171/PM/2006 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
European Mathematical Society |
publisher.none.fl_str_mv |
European Mathematical Society |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799137617616306176 |