Comparison triangle (original) (raw)
Define as the 2-dimensional metric space of constant curvature . So, for example, is the Euclidean plane, is the surface of the unit sphere, and is the hyperbolic plane. Let be a metric space. Let be a triangle in , with vertices , and . A comparison triangle in for is a triangle in with vertices , and such that , and . Such a triangle is unique up to isometry. The interior angle of at is called the comparison angle between and at . This is well-defined provided and are both distinct from .
| Property | Value |
|---|---|
| dbo:abstract | Define as the 2-dimensional metric space of constant curvature . So, for example, is the Euclidean plane, is the surface of the unit sphere, and is the hyperbolic plane. Let be a metric space. Let be a triangle in , with vertices , and . A comparison triangle in for is a triangle in with vertices , and such that , and . Such a triangle is unique up to isometry. The interior angle of at is called the comparison angle between and at . This is well-defined provided and are both distinct from . (en) |
| dbo:wikiPageID | 5845706 (xsd:integer) |
| dbo:wikiPageLength | 1250 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 783533182 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Constant_curvature dbr:Unit_sphere dbr:Curvature dbr:Isometry dbr:Hyperbolic_geometry dbc:Metric_geometry dbr:Triangle dbr:Metric_space dbr:Euclidean_plane dbr:2-dimensional dbr:Interior_angle dbr:A_Haefliger |
| dbp:wikiPageUsesTemplate | dbt:ISBN |
| dcterms:subject | dbc:Metric_geometry |
| rdfs:comment | Define as the 2-dimensional metric space of constant curvature . So, for example, is the Euclidean plane, is the surface of the unit sphere, and is the hyperbolic plane. Let be a metric space. Let be a triangle in , with vertices , and . A comparison triangle in for is a triangle in with vertices , and such that , and . Such a triangle is unique up to isometry. The interior angle of at is called the comparison angle between and at . This is well-defined provided and are both distinct from . (en) |
| rdfs:label | Comparison triangle (en) |
| owl:sameAs | freebase:Comparison triangle wikidata:Comparison triangle https://global.dbpedia.org/id/4htzL |
| prov:wasDerivedFrom | wikipedia-en:Comparison_triangle?oldid=783533182&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Comparison_triangle |
| is dbo:wikiPageRedirects of | dbr:Comparison_angle |
| is dbo:wikiPageWikiLink of | dbr:Comparison_theorem dbr:Busemann_function dbr:CAT(k)_space dbr:Non-positive_curvature dbr:Comparison_angle |
| is foaf:primaryTopic of | wikipedia-en:Comparison_triangle |