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- Ideal_point abstract "In hyperbolic geometry, an ideal point, omega point or point at infinity is a well defined point outside the hyperbolic plane or space.Given a line l and a point P not on l, right- and left-limiting parallels to l through P converge to l at ideal points.Unlike the projective case, ideal points form a boundary, not a submanifold. So, these lines do not intersect at an ideal point and such points, although well defined, do not belong to the hyperbolic space itself.The ideal points together form the Cayley absolute or boundary of a hyperbolic geometry. For instance, the unit circle forms the Cayley absolute of the Poincaré disk model and the Klein disk model.While the real line forms the Cayley absolute of the Poincaré half-plane model .Pasch's axiom and the exterior angle theorem still hold for an omega triangle, defined by two points in hyperbolic space and an omega point.".
- Ideal_point thumbnail Ideal_circles.GIF?width=300.
- Ideal_point wikiPageID "4995922".
- Ideal_point wikiPageLength "6919".
- Ideal_point wikiPageOutDegree "44".
- Ideal_point wikiPageRevisionID "701221708".
- Ideal_point wikiPageWikiLink Arc_(geometry).
- Ideal_point wikiPageWikiLink Beltrami–Klein_model.
- Ideal_point wikiPageWikiLink Category:Hyperbolic_geometry.
- Ideal_point wikiPageWikiLink Category:Infinity.
- Ideal_point wikiPageWikiLink Cayley–Klein_metric.
- Ideal_point wikiPageWikiLink Concentric.
- Ideal_point wikiPageWikiLink Exterior_angle_theorem.
- Ideal_point wikiPageWikiLink File:Ideal_circles.GIF.
- Ideal_point wikiPageWikiLink Horocycle.
- Ideal_point wikiPageWikiLink Horosphere.
- Ideal_point wikiPageWikiLink Hyperbolic_geometry.
- Ideal_point wikiPageWikiLink Hyperbolic_triangle.
- Ideal_point wikiPageWikiLink Hyperboloid_model.
- Ideal_point wikiPageWikiLink Hyperplane_at_infinity.
- Ideal_point wikiPageWikiLink Ideal_triangle.
- Ideal_point wikiPageWikiLink Limit_(mathematics).
- Ideal_point wikiPageWikiLink Limiting_parallel.
- Ideal_point wikiPageWikiLink Line_(geometry).
- Ideal_point wikiPageWikiLink Manifold.
- Ideal_point wikiPageWikiLink Paschs_axiom.
- Ideal_point wikiPageWikiLink Perpendicular.
- Ideal_point wikiPageWikiLink Poincaré_disk_model.
- Ideal_point wikiPageWikiLink Poincaré_half-plane_model.
- Ideal_point wikiPageWikiLink Quadrilateral.
- Ideal_point wikiPageWikiLink Unit_circle.
- Ideal_point wikiPageWikiLink Unit_sphere.
- Ideal_point wikiPageWikiLink Well-defined.
- Ideal_point wikiPageWikiLinkText "Ideal point".
- Ideal_point wikiPageWikiLinkText "Ideal point".
- Ideal_point wikiPageWikiLinkText "ideal (end) points".
- Ideal_point wikiPageWikiLinkText "ideal boundary".
- Ideal_point wikiPageWikiLinkText "ideal endpoints".
- Ideal_point wikiPageWikiLinkText "ideal point".
- Ideal_point wikiPageWikiLinkText "ideal".
- Ideal_point wikiPageUsesTemplate Template:About.
- Ideal_point wikiPageUsesTemplate Template:Interlanguage_link.
- Ideal_point wikiPageUsesTemplate Template:Main.
- Ideal_point wikiPageUsesTemplate Template:Reflist.
- Ideal_point subject Category:Hyperbolic_geometry.
- Ideal_point subject Category:Infinity.
- Ideal_point type Redirect.
- Ideal_point comment "In hyperbolic geometry, an ideal point, omega point or point at infinity is a well defined point outside the hyperbolic plane or space.Given a line l and a point P not on l, right- and left-limiting parallels to l through P converge to l at ideal points.Unlike the projective case, ideal points form a boundary, not a submanifold.".
- Ideal_point label "Ideal point".
- Ideal_point sameAs m.013f7ztk.
- Ideal_point wasDerivedFrom Ideal_point?oldid=701221708.
- Ideal_point depiction Ideal_circles.GIF.
- Ideal_point isPrimaryTopicOf Ideal_point.