| dbo:abstract |
In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space. When n = 8, the set of all such locations is called 8-dimensional space. Often such spaces are studied as vector spaces, without any notion of distance. Eight-dimensional Euclidean space is eight-dimensional space equipped with the Euclidean metric. More generally the term may refer to an eight-dimensional vector space over any field, such as an eight-dimensional complex vector space, which has 16 real dimensions. It may also refer to an eight-dimensional manifold such as an 8-sphere, or a variety of other geometric constructions. (en) 在數學中， 一個n實數的序列可以被理解為n維空間中的一個位置。當n等於八時，所有這樣的位置的集合被稱為八維空間。 通常這種空間被研究為一個向量空間，而沒有任何距離的概念。八維歐幾里得空間是一個配備了一個歐幾里得距離的八維空間，它由點積定義。 更廣義的來說，該術語可以指任何體上的八維向量空間，例如八維複矢量空間，其實際有著十六個維度。 它同時也可能指八維流形例如，或其它各種幾何構造。 (zh) |
| dbo:thumbnail |
wiki-commons:Special:FilePath/8-simplex_t0.svg?width=300 |
| dbo:wikiPageExternalLink |
http://nugae.wordpress.com/2007/04/25/on-quaternions-and-octonions/ http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/kiss.html http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html |
| dbo:wikiPageID |
25555117 (xsd:integer) |
| dbo:wikiPageLength |
7197 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
1096217026 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbr:Quaternion dbr:Euclidean_metric dbr:Algebra_of_physical_space dbc:Multi-dimensional_geometry dbr:Hurwitz's_theorem_(composition_algebras) dbr:Vector_space dbr:Complex_number dbr:Mathematics dbr:Clifford_algebra dbr:N-sphere dbr:Point_(geometry) dbr:1_42_polytope dbr:8-cube dbr:8-demicube dbr:8-orthoplex dbr:8-simplex dbc:8_(number) dbr:William_Rowan_Hamilton dbr:Division_algebra dbr:Coxeter-Dynkin_diagram dbr:Lattice_(group) dbr:2_41_polytope dbr:240_(number) dbr:4_21_polytope dbr:E8_(mathematics) dbr:Euclidean_space dbr:Field_(mathematics) dbr:Dimension_(vector_space) dbr:Regular_polytope dbc:Dimension dbr:Harold_Scott_MacDonald_Coxeter dbr:Isomorphic dbr:Coxeter_group dbr:Biquaternion dbr:Manifold dbr:Special_relativity dbr:Springer_Science+Business_Media dbr:Neil_Sloane dbr:Real_number dbr:Warren_Siegel dbr:Kissing_number_problem dbr:Uniform_8-polytope dbr:Polytope dbr:Spacetime_algebra dbr:List_of_regular_polytopes dbr:8-sphere dbr:Normed_division_algebra dbr:Pauli_algebra dbr:File:8-simplex_t0.svg dbr:File:Gosset_1_42_polytope_petrie.svg dbr:File:2_41_t0_E8.svg dbr:File:4_21_t0_E8.svg dbr:File:8-cube_t0.svg dbr:File:8-cube_t7.svg dbr:File:8-demicube_t0_D7.svg |
| dbp:wikiPageUsesTemplate |
dbt:CDD dbt:Citation dbt:ISBN dbt:Main dbt:Math dbt:Reflist dbt:Short_description dbt:Dimension_topics |
| dct:subject |
dbc:Multi-dimensional_geometry dbc:8_(number) dbc:Dimension |
| rdfs:comment |
在數學中， 一個n實數的序列可以被理解為n維空間中的一個位置。當n等於八時，所有這樣的位置的集合被稱為八維空間。 通常這種空間被研究為一個向量空間，而沒有任何距離的概念。八維歐幾里得空間是一個配備了一個歐幾里得距離的八維空間，它由點積定義。 更廣義的來說，該術語可以指任何體上的八維向量空間，例如八維複矢量空間，其實際有著十六個維度。 它同時也可能指八維流形例如，或其它各種幾何構造。 (zh) In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space. When n = 8, the set of all such locations is called 8-dimensional space. Often such spaces are studied as vector spaces, without any notion of distance. Eight-dimensional Euclidean space is eight-dimensional space equipped with the Euclidean metric. (en) |
| rdfs:label |
Eight-dimensional space (en) 八维空间 (zh) |
| owl:sameAs |
freebase:Eight-dimensional space wikidata:Eight-dimensional space dbpedia-fa:Eight-dimensional space dbpedia-zh:Eight-dimensional space https://global.dbpedia.org/id/9ukq |
| prov:wasDerivedFrom |
wikipedia-en:Eight-dimensional_space?oldid=1096217026&ns=0 |
| foaf:depiction |
wiki-commons:Special:FilePath/8-simplex_t0.svg wiki-commons:Special:FilePath/4_21_t0_E8.svg wiki-commons:Special:FilePath/2_41_t0_E8.svg wiki-commons:Special:FilePath/Gosset_1_42_polytope_petrie.svg wiki-commons:Special:FilePath/8-demicube_t0_D7.svg wiki-commons:Special:FilePath/8-cube_t0.svg wiki-commons:Special:FilePath/8-cube_t7.svg |
| foaf:isPrimaryTopicOf |
wikipedia-en:Eight-dimensional_space |
| is dbo:wikiPageRedirects of |
dbr:8-dimensional_space dbr:8th_dimension dbr:Eight-dimensional dbr:Eighth_dimension |
| is dbo:wikiPageWikiLink of |
dbr:8D dbr:List_of_acronyms:_0–9 dbr:List_of_mathematical_shapes dbr:List_of_polygons,_polyhedra_and_polytopes dbr:Omnitruncated_8-simplex_honeycomb dbr:Quarter_8-cubic_honeycomb dbr:8-dimensional_space dbr:Split-biquaternion dbr:Uniform_8-polytope dbr:8th_dimension dbr:Eight-dimensional dbr:Eighth_dimension |
| is foaf:primaryTopic of |
wikipedia-en:Eight-dimensional_space |
