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- Point_at_infinity abstract "In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.In the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane. Adjoining these points produces a projective plane, in which no point can be distinguished, if we "forget" which points were added. This holds for a geometry over any field, and more generally over any division ring.In the real case, a point at infinity completes a line into a topologically closed curve. In higher dimensions, all the points at infinity form a projective subspace of one dimension less than that of the whole projective space to which they belong. A point at infinity can also be added to the complex line (which may be thought of as the complex plane), thereby turning it into a closed surface known as the complex projective line, CP1, also called the Riemann sphere (when complex numbers are mapped to each point).In the case of a hyperbolic space, each line has two distinct ideal points. Here, the set of ideal points takes the form of a quadric.".
- Point_at_infinity thumbnail Real_projective_line.svg?width=300.
- Point_at_infinity wikiPageID "403139".
- Point_at_infinity wikiPageLength "4205".
- Point_at_infinity wikiPageOutDegree "38".
- Point_at_infinity wikiPageRevisionID "673628864".
- Point_at_infinity wikiPageWikiLink Affine_plane.
- Point_at_infinity wikiPageWikiLink Affine_space.
- Point_at_infinity wikiPageWikiLink Alexandroff_extension.
- Point_at_infinity wikiPageWikiLink Asymptote.
- Point_at_infinity wikiPageWikiLink Asymtote.
- Point_at_infinity wikiPageWikiLink Category:Hyperbolic_geometry.
- Point_at_infinity wikiPageWikiLink Category:Infinity.
- Point_at_infinity wikiPageWikiLink Category:Projective_geometry.
- Point_at_infinity wikiPageWikiLink Cayley_absolute.
- Point_at_infinity wikiPageWikiLink Cayley–Klein_metric.
- Point_at_infinity wikiPageWikiLink Compact_space.
- Point_at_infinity wikiPageWikiLink Compactification_(mathematics).
- Point_at_infinity wikiPageWikiLink Complex_line.
- Point_at_infinity wikiPageWikiLink Convergence.
- Point_at_infinity wikiPageWikiLink Division_by_zero.
- Point_at_infinity wikiPageWikiLink Division_ring.
- Point_at_infinity wikiPageWikiLink Euclidean_plane.
- Point_at_infinity wikiPageWikiLink Euclidean_space.
- Point_at_infinity wikiPageWikiLink Field_(mathematics).
- Point_at_infinity wikiPageWikiLink Geometry.
- Point_at_infinity wikiPageWikiLink Hyperbolic_geometry.
- Point_at_infinity wikiPageWikiLink Hyperbolic_plane.
- Point_at_infinity wikiPageWikiLink Hyperbolic_space.
- Point_at_infinity wikiPageWikiLink Hyperplane_at_infinity.
- Point_at_infinity wikiPageWikiLink Ideal_point.
- Point_at_infinity wikiPageWikiLink Limiting_parallel.
- Point_at_infinity wikiPageWikiLink Line_at_infinity.
- Point_at_infinity wikiPageWikiLink Manifold.
- Point_at_infinity wikiPageWikiLink Pencil_(mathematics).
- Point_at_infinity wikiPageWikiLink Plane_at_infinity.
- Point_at_infinity wikiPageWikiLink Projective_plane.
- Point_at_infinity wikiPageWikiLink Projective_space.
- Point_at_infinity wikiPageWikiLink Quadric_(projective_geometry).
- Point_at_infinity wikiPageWikiLink Real_line.
- Point_at_infinity wikiPageWikiLink Riemann_sphere.
- Point_at_infinity wikiPageWikiLink Singular_point_of_an_algebraic_variety.
- Point_at_infinity wikiPageWikiLink Smooth_algebraic_variety.
- Point_at_infinity wikiPageWikiLink Topological_space.
- Point_at_infinity wikiPageWikiLink Two-dimensional_space.
- Point_at_infinity wikiPageWikiLink Vanishing_point.
- Point_at_infinity wikiPageWikiLink File:Real_projective_line.svg.
- Point_at_infinity wikiPageWikiLinkText "(unsigned) infinity".
- Point_at_infinity wikiPageWikiLinkText "Point at infinity".
- Point_at_infinity wikiPageWikiLinkText "at infinity".
- Point_at_infinity wikiPageWikiLinkText "ideal point".
- Point_at_infinity wikiPageWikiLinkText "infinite".
- Point_at_infinity wikiPageWikiLinkText "infinity".
- Point_at_infinity wikiPageWikiLinkText "objects "at infinity"".
- Point_at_infinity wikiPageWikiLinkText "point ''at infinity''".
- Point_at_infinity wikiPageWikiLinkText "point at infinity".
- Point_at_infinity wikiPageWikiLinkText "point labeled ".
- Point_at_infinity wikiPageWikiLinkText "point".
- Point_at_infinity wikiPageWikiLinkText "points at infinity".
- Point_at_infinity wikiPageWikiLinkText "points".
- Point_at_infinity wikiPageWikiLinkText "spatial infinity".
- Point_at_infinity wikiPageWikiLinkText "unsigned infinity".
- Point_at_infinity hasPhotoCollection Point_at_infinity.
- Point_at_infinity wikiPageUsesTemplate Template:Main.
- Point_at_infinity wikiPageUsesTemplate Template:Multi-section_link.
- Point_at_infinity wikiPageUsesTemplate Template:Mvar.
- Point_at_infinity wikiPageUsesTemplate Template:Unreferenced.
- Point_at_infinity subject Category:Hyperbolic_geometry.
- Point_at_infinity subject Category:Infinity.
- Point_at_infinity subject Category:Projective_geometry.
- Point_at_infinity hypernym Point.
- Point_at_infinity type Place.
- Point_at_infinity comment "In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.In the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane. Adjoining these points produces a projective plane, in which no point can be distinguished, if we "forget" which points were added.".
- Point_at_infinity label "Point at infinity".
- Point_at_infinity sameAs كيانات_هندسية_لانهائية.
- Point_at_infinity sameAs Nevlastní_bod.
- Point_at_infinity sameAs Fernelement.
- Point_at_infinity sameAs Punto_del_infinito.
- Point_at_infinity sameAs Point_xc3xa0_linfini.
- Point_at_infinity sameAs Enti_geometrici_impropri.
- Point_at_infinity sameAs 無限遠点.
- Point_at_infinity sameAs 무한_원점.
- Point_at_infinity sameAs Punt_op_oneindig.
- Point_at_infinity sameAs Ponto_impróprio.
- Point_at_infinity sameAs m.024325.
- Point_at_infinity sameAs Бесконечно_удалённая_точка_(значения).
- Point_at_infinity sameAs Točka_v_neskončnosti.
- Point_at_infinity sameAs Q1191139.
- Point_at_infinity sameAs Q1191139.
- Point_at_infinity sameAs 无穷远点.
- Point_at_infinity wasDerivedFrom Point_at_infinity?oldid=673628864.
- Point_at_infinity depiction Real_projective_line.svg.
- Point_at_infinity isPrimaryTopicOf Point_at_infinity.