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• Spherical_geometry abstract "Spherical geometry is the geometry of the two-dimensional surface of a sphere. It is an example of a geometry which is not Euclidean. Two practical applications of the principles of spherical geometry are to navigation and astronomy.In plane geometry the basic concepts are points and (straight) lines. On the sphere, points are defined in the usual sense. The equivalents of lines are not defined in the usual sense of "straight line" in Euclidean geometry but in the sense of "the shortest paths between points," which are called geodesics. On the sphere the geodesics are the great circles; other geometric concepts are defined as in plane geometry but with straight lines replaced by great circles. Thus, in spherical geometry angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a triangle exceeds 180 degrees.Spherical geometry is not elliptic geometry but shares with that geometry the property that a line has no parallels through a given point. Contrast this with Euclidean geometry, in which a line has one parallel through a given point, and hyperbolic geometry, in which a line has two parallels and an infinite number of ultraparallels through a given point.An important geometry related to that of the sphere is that of the real projective plane; it is obtained by identifying antipodal points (pairs of opposite points) on the sphere. (This is elliptic geometry.) Locally, the projective plane has all the properties of spherical geometry, but it has different global properties. In particular, it is non-orientable, or one-sided.Concepts of spherical geometry may also be applied to the oblong sphere, though minor modifications must be implemented on certain formulas.Higher-dimensional spherical geometries exist; see elliptic geometry.".
• Spherical_geometry thumbnail Triangles_(spherical_geometry).jpg?width=300.
• Spherical_geometry wikiPageExternalLink sphere.
• Spherical_geometry wikiPageExternalLink navigation_triangles.html.
• Spherical_geometry wikiPageExternalLink sphaerica.
• Spherical_geometry wikiPageID "174026".
• Spherical_geometry wikiPageRevisionID "601331250".
• Spherical_geometry hasPhotoCollection Spherical_geometry.
• Spherical_geometry title "Spherical Geometry".
• Spherical_geometry urlname "SphericalGeometry".
• Spherical_geometry subject Category:Classical_geometry.
• Spherical_geometry subject Category:Spherical_astronomy.
• Spherical_geometry subject Category:Spherical_geometry.
• Spherical_geometry subject Category:Spherical_trigonometry.
• Spherical_geometry comment "Spherical geometry is the geometry of the two-dimensional surface of a sphere. It is an example of a geometry which is not Euclidean. Two practical applications of the principles of spherical geometry are to navigation and astronomy.In plane geometry the basic concepts are points and (straight) lines. On the sphere, points are defined in the usual sense.".
• Spherical_geometry label "Bolmeetkunde".
• Spherical_geometry label "Geometria esférica".
• Spherical_geometry label "Geometria sferica".
• Spherical_geometry label "Geometria sferyczna".
• Spherical_geometry label "Geometría esférica".
• Spherical_geometry label "Géométrie sphérique".
• Spherical_geometry label "Spherical geometry".
• Spherical_geometry label "Sphärische Geometrie".
• Spherical_geometry label "Сферическая геометрия".
• Spherical_geometry label "هندسة كروية".
• Spherical_geometry label "球面幾何学".
• Spherical_geometry label "球面幾何學".
• Spherical_geometry sameAs Sférická_geometrie.
• Spherical_geometry sameAs Sphärische_Geometrie.
• Spherical_geometry sameAs Σφαιρική_γεωμετρία.
• Spherical_geometry sameAs Geometría_esférica.
• Spherical_geometry sameAs Géométrie_sphérique.
• Spherical_geometry sameAs Geometri_bola.
• Spherical_geometry sameAs Geometria_sferica.
• Spherical_geometry sameAs 球面幾何学.
• Spherical_geometry sameAs 구면기하학.
• Spherical_geometry sameAs Bolmeetkunde.
• Spherical_geometry sameAs Geometria_sferyczna.
• Spherical_geometry sameAs Geometria_esférica.
• Spherical_geometry sameAs m.017h21.
• Spherical_geometry sameAs Q326905.
• Spherical_geometry sameAs Q326905.
• Spherical_geometry wasDerivedFrom Spherical_geometry?oldid=601331250.
• Spherical_geometry depiction Triangles_(spherical_geometry).jpg.
• Spherical_geometry isPrimaryTopicOf Spherical_geometry.