@prefix rdf: . @prefix dbr: . @prefix yago: . dbr:Euclidean_group rdf:type yago:WikicatLieGroups , yago:Symmetry105064827 , yago:Attribute100024264 . @prefix owl: . dbr:Euclidean_group rdf:type owl:Thing , yago:SpatialProperty105062748 , yago:WikicatEuclideanSymmetries , yago:Group100031264 , yago:Property104916342 , yago:Abstraction100002137 . @prefix dbo: . dbr:Euclidean_group rdf:type dbo:Band . @prefix rdfs: . dbr:Euclidean_group rdfs:label "Euklidische Gruppe"@de , "\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u306E\u904B\u52D5\u7FA4"@ja , "Eukleidova grupa"@cs , "Euclidean group"@en , "Isom\u00E9trie affine"@fr , "Grupo eucl\u00EDdeo"@es , "Grupo euclidiano"@pt , "\u6B27\u51E0\u91CC\u5F97\u7FA4"@zh , "Euclidische groep"@nl , "\uC720\uD074\uB9AC\uB4DC \uAD70"@ko ; rdfs:comment "Grupo euclidiano \u00E9 o grupo de simetrias de um espa\u00E7o afim euclidiano. As simetrias do espa\u00E7o euclidiano (i.e., as transforma\u00E7\u00F5es geom\u00E9tricas que preservam as medidas das dist\u00E2ncias e dos \u00E2ngulos entre vetores) s\u00E3o as transla\u00E7\u00F5es, rota\u00E7\u00F5es e reflex\u00F5es."@pt , "In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space ; that is, the transformations of that space that preserve the Euclidean distance between any two points (also called Euclidean transformations). The group depends only on the dimension n of the space, and is commonly denoted E(n) or ISO(n). These groups are among the oldest and most studied, at least in the cases of dimension 2 and 3 \u2013 implicitly, long before the concept of group was invented."@en , "\u6570\u5B66\u4E2D\uFF0C\u6B27\u51E0\u91CC\u5F97\u7FA4 E(n)\uFF0C\u6216ISO(n)\u662Fn\u7EF4\u6B27\u6C0F\u7A7A\u95F4\u7684\u5BF9\u79F0\u7FA4\u3002\u5B83\u7684\u5143\u7D20\u4E0E\u57FA\u4E8E\u6B27\u6C0F\u8DDD\u79BB\u7684\u7B49\u8DDD\u540C\u6784\u76F8\u5173\uFF0C\u5E76\u88AB\u79F0\u4E3A\u6B27\u5F0F\u7B49\u8DDD\u540C\u6784\uFF0C\u6B27\u5F0F\u53D8\u6362\u6216\u3002"@zh , "Une isom\u00E9trie affine est une transformation bijective d'un espace affine euclidien dans un autre qui est \u00E0 la fois une application affine et une isom\u00E9trie (c'est-\u00E0-dire une bijection conservant les distances). Si cette isom\u00E9trie conserve aussi l'orientation, on dit que c'est un d\u00E9placement. Si elle inverse l'orientation, il s'agit d'un antid\u00E9placement. Les d\u00E9placements sont les compos\u00E9s de translations et rotations. Les r\u00E9flexions sont des antid\u00E9placements."@fr , "\uAE30\uD558\uD559\uC5D0\uC11C \uC720\uD074\uB9AC\uB4DC \uAD70(Euclid\u7FA4, \uC601\uC5B4: Euclidean group)\uC740 \uC720\uD074\uB9AC\uB4DC \uACF5\uAC04\uC758 \uB4F1\uAC70\uB9AC \uBCC0\uD658\uB4E4\uB85C \uAD6C\uC131\uB41C \uB9AC \uAD70\uC774\uB2E4. \uC989, \uAC70\uB9AC\uC640 \uAC01\uB3C4\uAC00 \uC815\uC758\uB418\uC9C0\uB9CC, \uC6D0\uC810\uC774 \uC815\uC758\uB418\uC9C0 \uC54A\uB294 \uC720\uD074\uB9AC\uB4DC \uACF5\uAC04\uC758 \uC774\uB2E4. (\uBCD1\uC9C4 \uBCC0\uD658)\uACFC \uC9C1\uAD50\uAD70(\uD68C\uC804)\uC758 \uBC18\uC9C1\uC811\uACF1\uC774\uB2E4."@ko , "Eukleidova grupa je v matematice mno\u017Eina v\u0161ech posunut\u00ED, rotac\u00ED a zrcadlen\u00ED Euklidova prostoru spolu s operac\u00ED skl\u00E1d\u00E1n\u00ED. Je to tedy mno\u017Eina v\u0161ech zobrazen\u00ED, kter\u00E9 zachov\u00E1vaj\u00ED vzd\u00E1lenosti, velikosti vektor\u016F a \u00FAhly. Pro n rozm\u011Brn\u00FD Euklid\u016Fv prostor se obvykle zna\u010D\u00ED"@cs , "In de groepentheorie, een deelgebied van de wiskunde, is de euclidische groep , soms ook wel genoemd, de symmetriegroep van de -dimensionale euclidische ruimte. De elementen van deze groep, de isometrie\u00EBn geassocieerd met de euclidische metriek, worden euclidische isometrie\u00EBn genoemd. Ze zijn van de vorm met een orthogonale matrix (dat wil zeggen ). De groep is een ondergroep van de affiene groep . De euclidische groepen tellen sinds lang, ruim voordat het concept van een groep expliciet werd geformuleerd, onder de oudste en meest bestudeerde, althans voor het geval van de dimensies 2 en 3."@nl , "\u6570\u5B66\u306B\u304A\u3051\u308B\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u7FA4\uFF08\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9-\u3050\u3093\u3001\u82F1: Euclidean group\uFF09\u3042\u308B\u3044\u306F\u904B\u52D5\u7FA4 (motion group) \u306F\u3001\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u7A7A\u9593\u306E\u3092\u8A00\u3046\u3002\u305D\u306E\u5143\u306F\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u8DDD\u96E2\u306B\u4ED8\u968F\u3059\u308B\u7B49\u9577\u5909\u63DB\u3067\u3042\u308A\u3001\u5408\u540C\u5909\u63DB\u3042\u308B\u3044\u306F\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u306E\u904B\u52D5 (motion) \u3068\u547C\u3070\u308C\u308B\u3002\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u306E\u904B\u52D5\u7FA4\u306E\u7814\u7A76\u306F\u3001\u5C11\u306A\u304F\u3068\u3082\u4E8C\u6B21\u5143\u3084\u4E09\u6B21\u5143\u306E\u5834\u5408\u306B\u3064\u3044\u3066\u306F\u6975\u3081\u3066\u53E4\u304F\u3001\u7FA4\u306E\u6982\u5FF5\u304C\u767A\u3059\u308B\u3088\u308A\u3082\u305A\u3063\u3068\u4EE5\u524D\u304B\u3089\uFF08\u5F93\u3063\u3066\u3082\u3061\u308D\u3093\u7FA4\u3068\u3057\u3066\u3067\u306A\u304F\u3001\u3082\u3063\u3068\u9670\u4F0F\u7684\u306A\u5F62\u3067\uFF09\u3088\u304F\u8ABF\u3079\u3089\u308C\u3066\u3044\u308B\u3002 n-\u6B21\u5143\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u7A7A\u9593\u306E\u904B\u52D5\u7FA4\u306F E(n) \u3084 iso(n) \u306A\u3069\u3068\u3082\u8868\u3055\u308C\u308B\u3002 \u4E09\u6B21\u5143\u307E\u3067\u306E\u7B49\u9577\u5909\u63DB\u306B\u3064\u3044\u3066\u306E\u6982\u89B3E(1), E(2), E(3) \u306F\u81EA\u7531\u5EA6\u306B\u3088\u3063\u3066\u4EE5\u4E0B\u306E\u3088\u3046\u306B\u5206\u985E\u3067\u304D\u308B: \u300C\u300D\u3082\u53C2\u7167 \u306F E+(3) \u306E\u4EFB\u610F\u306E\u5143\u304C\u87BA\u65CB\u5909\u4F4D\u3067\u3042\u308B\u3053\u3068\u3092\u4E3B\u5F35\u3059\u308B\u3002 \u300C\u4E09\u6B21\u5143\u76F4\u4EA4\u5909\u63DB\u7FA4|\u539F\u70B9\u3092\u56FA\u5B9A\u3059\u308B\u4E09\u6B21\u5143\u306E\u7B49\u8DDD\u5909\u63DB\u300D\u3001\u300C\u7A7A\u9593\u7FA4\u300D\u3001\u304A\u3088\u3073\u300C\u5BFE\u5408\u300D\u3082\u53C2\u7167"@ja , "En matem\u00E1ticas, un grupo eucl\u00EDdeo es el grupo caracter\u00EDstico de las isometr\u00EDas de un espacio eucl\u00EDdeo \U0001D53Cn; es decir, de las transformaciones de ese espacio que preservan la distancia euclidiana entre cualquier par de puntos (tambi\u00E9n llamadas ). La configuraci\u00F3n del grupo depende \u00FAnicamente de la dimensi\u00F3n n del espacio, y com\u00FAnmente se denota como E(n) o ISO(n). Este grupo est\u00E1 entre los m\u00E1s antiguos, al menos en los casos de dimensi\u00F3n 2 y 3 , siendo impl\u00EDcitamente estudiados mucho antes de que se ideara el concepto de grupo."@es ; rdfs:seeAlso dbr:Euclidean_plane_isometry . @prefix dcterms: . @prefix dbc: . dbr:Euclidean_group dcterms:subject dbc:Lie_groups , dbc:Euclidean_symmetries ; dbo:wikiPageID 652164 ; dbo:wikiPageRevisionID 1111504010 ; dbo:wikiPageWikiLink dbr:Square_matrix , dbr:Helix , dbc:Lie_groups , dbr:Rotation , dbr:Affine_group , , , dbr:Isometry , dbr:Affine_transformation , dbr:Glide_plane , dbr:Glide_reflection , , dbr:Fixed_points_of_isometry_groups_in_Euclidean_space , dbr:Column_vector , , dbr:Euclidean_space , dbr:Dihedral_group , dbr:Affine_geometry , dbr:Improper_rotation , dbr:Plane_of_rotation , dbr:Coset , dbr:Distance , dbr:Reflection_through_the_origin , dbr:Euclidean_transformation , dbr:Rotational_symmetry , dbr:Discrete_space , dbr:Translational_symmetry , dbr:Calculus , dbr:Normal_subgroup , , dbr:Screw_displacement , dbr:Rigid_motion , dbr:Symmetry_group , dbr:Topological_group , , , dbr:Erlangen_programme , dbr:Mathematics , , dbr:William_Thurston , dbr:Special_orthogonal_group , dbr:Topology , dbr:Mirror , , , dbr:Classical_mechanics , dbr:Angle , dbr:Identity_transformation , , dbc:Euclidean_symmetries , dbr:Semidirect_product , dbr:Index_of_a_subgroup , dbr:Finite_group , dbr:Coordinate_rotations_and_reflections , dbr:Function_composition , , dbr:Space_group , dbr:Lie_group , dbr:Quotient_group , dbr:Euclidean_distance , dbr:Euclidean_geometry , dbr:Conjugacy_class , dbr:Orthogonal_group , dbr:Euclidean_plane_isometry , dbr:Felix_Klein , , dbr:Rigid_body , dbr:Orthogonal_matrix , dbr:Subgroup . @prefix ns8: . dbr:Euclidean_group dbo:wikiPageExternalLink ns8:n153 , ; owl:sameAs . @prefix dbpedia-cs: . dbr:Euclidean_group owl:sameAs dbpedia-cs:Eukleidova_grupa . @prefix yago-res: . dbr:Euclidean_group owl:sameAs yago-res:Euclidean_group , , . @prefix wikidata: . dbr:Euclidean_group owl:sameAs wikidata:Q852195 , , . @prefix dbpedia-pt: . dbr:Euclidean_group owl:sameAs dbpedia-pt:Grupo_euclidiano , . @prefix dbpedia-de: . dbr:Euclidean_group owl:sameAs dbpedia-de:Euklidische_Gruppe , . @prefix dbpedia-nl: . dbr:Euclidean_group owl:sameAs dbpedia-nl:Euclidische_groep . @prefix dbp: . @prefix dbt: . dbr:Euclidean_group dbp:wikiPageUsesTemplate dbt:Clarify , dbt:Lie_groups , dbt:See_also , dbt:Radic , dbt:ISBN , dbt:Group_theory_sidebar , dbt:No , dbt:Cite_book , dbt:Short_description , dbt:Math , dbt:Yes ; dbo:abstract "\u6570\u5B66\u4E2D\uFF0C\u6B27\u51E0\u91CC\u5F97\u7FA4 E(n)\uFF0C\u6216ISO(n)\u662Fn\u7EF4\u6B27\u6C0F\u7A7A\u95F4\u7684\u5BF9\u79F0\u7FA4\u3002\u5B83\u7684\u5143\u7D20\u4E0E\u57FA\u4E8E\u6B27\u6C0F\u8DDD\u79BB\u7684\u7B49\u8DDD\u540C\u6784\u76F8\u5173\uFF0C\u5E76\u88AB\u79F0\u4E3A\u6B27\u5F0F\u7B49\u8DDD\u540C\u6784\uFF0C\u6B27\u5F0F\u53D8\u6362\u6216\u3002"@zh , "Une isom\u00E9trie affine est une transformation bijective d'un espace affine euclidien dans un autre qui est \u00E0 la fois une application affine et une isom\u00E9trie (c'est-\u00E0-dire une bijection conservant les distances). Si cette isom\u00E9trie conserve aussi l'orientation, on dit que c'est un d\u00E9placement. Si elle inverse l'orientation, il s'agit d'un antid\u00E9placement. Les d\u00E9placements sont les compos\u00E9s de translations et rotations. Les r\u00E9flexions sont des antid\u00E9placements."@fr , "In de groepentheorie, een deelgebied van de wiskunde, is de euclidische groep , soms ook wel genoemd, de symmetriegroep van de -dimensionale euclidische ruimte. De elementen van deze groep, de isometrie\u00EBn geassocieerd met de euclidische metriek, worden euclidische isometrie\u00EBn genoemd. Ze zijn van de vorm met een orthogonale matrix (dat wil zeggen ). De groep is een ondergroep van de affiene groep . De euclidische groepen tellen sinds lang, ruim voordat het concept van een groep expliciet werd geformuleerd, onder de oudste en meest bestudeerde, althans voor het geval van de dimensies 2 en 3."@nl , "Eukleidova grupa je v matematice mno\u017Eina v\u0161ech posunut\u00ED, rotac\u00ED a zrcadlen\u00ED Euklidova prostoru spolu s operac\u00ED skl\u00E1d\u00E1n\u00ED. Je to tedy mno\u017Eina v\u0161ech zobrazen\u00ED, kter\u00E9 zachov\u00E1vaj\u00ED vzd\u00E1lenosti, velikosti vektor\u016F a \u00FAhly. Pro n rozm\u011Brn\u00FD Euklid\u016Fv prostor se obvykle zna\u010D\u00ED"@cs , "Grupo euclidiano \u00E9 o grupo de simetrias de um espa\u00E7o afim euclidiano. As simetrias do espa\u00E7o euclidiano (i.e., as transforma\u00E7\u00F5es geom\u00E9tricas que preservam as medidas das dist\u00E2ncias e dos \u00E2ngulos entre vetores) s\u00E3o as transla\u00E7\u00F5es, rota\u00E7\u00F5es e reflex\u00F5es."@pt , "En matem\u00E1ticas, un grupo eucl\u00EDdeo es el grupo caracter\u00EDstico de las isometr\u00EDas de un espacio eucl\u00EDdeo \U0001D53Cn; es decir, de las transformaciones de ese espacio que preservan la distancia euclidiana entre cualquier par de puntos (tambi\u00E9n llamadas ). La configuraci\u00F3n del grupo depende \u00FAnicamente de la dimensi\u00F3n n del espacio, y com\u00FAnmente se denota como E(n) o ISO(n). El grupo eucl\u00EDdeo E(n) comprende todas las traslaciones, rotaciones y reflexiones de \U0001D53Cn; y las combinaciones finitas arbitrarias de estas transformaciones. El grupo euclidiano puede verse como el grupo de simetr\u00EDa del espacio en s\u00ED, y contiene el grupo de simetr\u00EDas de cualquier figura (subconjunto) de ese espacio. Una isometr\u00EDa euclidiana puede ser directa o indirecta, dependiendo de si conserva la paridad de las figuras. Las isometr\u00EDas euclidianas directas forman un subgrupo, el grupo euclidiano especial, cuyos elementos se denominan o movimientos euclidianos. Comprenden combinaciones arbitrarias de traslaciones y rotaciones, pero no de reflexiones. Este grupo est\u00E1 entre los m\u00E1s antiguos, al menos en los casos de dimensi\u00F3n 2 y 3 , siendo impl\u00EDcitamente estudiados mucho antes de que se ideara el concepto de grupo."@es , "\u6570\u5B66\u306B\u304A\u3051\u308B\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u7FA4\uFF08\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9-\u3050\u3093\u3001\u82F1: Euclidean group\uFF09\u3042\u308B\u3044\u306F\u904B\u52D5\u7FA4 (motion group) \u306F\u3001\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u7A7A\u9593\u306E\u3092\u8A00\u3046\u3002\u305D\u306E\u5143\u306F\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u8DDD\u96E2\u306B\u4ED8\u968F\u3059\u308B\u7B49\u9577\u5909\u63DB\u3067\u3042\u308A\u3001\u5408\u540C\u5909\u63DB\u3042\u308B\u3044\u306F\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u306E\u904B\u52D5 (motion) \u3068\u547C\u3070\u308C\u308B\u3002\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u306E\u904B\u52D5\u7FA4\u306E\u7814\u7A76\u306F\u3001\u5C11\u306A\u304F\u3068\u3082\u4E8C\u6B21\u5143\u3084\u4E09\u6B21\u5143\u306E\u5834\u5408\u306B\u3064\u3044\u3066\u306F\u6975\u3081\u3066\u53E4\u304F\u3001\u7FA4\u306E\u6982\u5FF5\u304C\u767A\u3059\u308B\u3088\u308A\u3082\u305A\u3063\u3068\u4EE5\u524D\u304B\u3089\uFF08\u5F93\u3063\u3066\u3082\u3061\u308D\u3093\u7FA4\u3068\u3057\u3066\u3067\u306A\u304F\u3001\u3082\u3063\u3068\u9670\u4F0F\u7684\u306A\u5F62\u3067\uFF09\u3088\u304F\u8ABF\u3079\u3089\u308C\u3066\u3044\u308B\u3002 n-\u6B21\u5143\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u7A7A\u9593\u306E\u904B\u52D5\u7FA4\u306F E(n) \u3084 iso(n) \u306A\u3069\u3068\u3082\u8868\u3055\u308C\u308B\u3002 \u4E09\u6B21\u5143\u307E\u3067\u306E\u7B49\u9577\u5909\u63DB\u306B\u3064\u3044\u3066\u306E\u6982\u89B3E(1), E(2), E(3) \u306F\u81EA\u7531\u5EA6\u306B\u3088\u3063\u3066\u4EE5\u4E0B\u306E\u3088\u3046\u306B\u5206\u985E\u3067\u304D\u308B: \u300C\u300D\u3082\u53C2\u7167 \u306F E+(3) \u306E\u4EFB\u610F\u306E\u5143\u304C\u87BA\u65CB\u5909\u4F4D\u3067\u3042\u308B\u3053\u3068\u3092\u4E3B\u5F35\u3059\u308B\u3002 \u300C\u4E09\u6B21\u5143\u76F4\u4EA4\u5909\u63DB\u7FA4|\u539F\u70B9\u3092\u56FA\u5B9A\u3059\u308B\u4E09\u6B21\u5143\u306E\u7B49\u8DDD\u5909\u63DB\u300D\u3001\u300C\u7A7A\u9593\u7FA4\u300D\u3001\u304A\u3088\u3073\u300C\u5BFE\u5408\u300D\u3082\u53C2\u7167"@ja , "\uAE30\uD558\uD559\uC5D0\uC11C \uC720\uD074\uB9AC\uB4DC \uAD70(Euclid\u7FA4, \uC601\uC5B4: Euclidean group)\uC740 \uC720\uD074\uB9AC\uB4DC \uACF5\uAC04\uC758 \uB4F1\uAC70\uB9AC \uBCC0\uD658\uB4E4\uB85C \uAD6C\uC131\uB41C \uB9AC \uAD70\uC774\uB2E4. \uC989, \uAC70\uB9AC\uC640 \uAC01\uB3C4\uAC00 \uC815\uC758\uB418\uC9C0\uB9CC, \uC6D0\uC810\uC774 \uC815\uC758\uB418\uC9C0 \uC54A\uB294 \uC720\uD074\uB9AC\uB4DC \uACF5\uAC04\uC758 \uC774\uB2E4. (\uBCD1\uC9C4 \uBCC0\uD658)\uACFC \uC9C1\uAD50\uAD70(\uD68C\uC804)\uC758 \uBC18\uC9C1\uC811\uACF1\uC774\uB2E4."@ko , "In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space ; that is, the transformations of that space that preserve the Euclidean distance between any two points (also called Euclidean transformations). The group depends only on the dimension n of the space, and is commonly denoted E(n) or ISO(n). The Euclidean group E(n) comprises all translations, rotations, and reflections of ; and arbitrary finite combinations of them. The Euclidean group can be seen as the symmetry group of the space itself, and contains the group of symmetries of any figure (subset) of that space. A Euclidean isometry can be direct or indirect, depending on whether it preserves the handedness of figures. The direct Euclidean isometries form a subgroup, the special Euclidean group, often denoted SE(n), whose elements are called rigid motions or Euclidean motions. They comprise arbitrary combinations of translations and rotations, but not reflections. These groups are among the oldest and most studied, at least in the cases of dimension 2 and 3 \u2013 implicitly, long before the concept of group was invented."@en . @prefix gold: . dbr:Euclidean_group gold:hypernym dbr:Group . @prefix prov: . dbr:Euclidean_group prov:wasDerivedFrom . @prefix xsd: . dbr:Euclidean_group dbo:wikiPageLength "16096"^^xsd:nonNegativeInteger . @prefix foaf: . @prefix wikipedia-en: . dbr:Euclidean_group foaf:isPrimaryTopicOf wikipedia-en:Euclidean_group .