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- Horocycle abstract "In hyperbolic geometry, a horocycle (Greek: ὅριον + κύκλος — border + circle, sometimes called an oricycle , oricircle, or limit circle ) is a curve whose normal or perpendicular geodesics all converge asymptotically in the same direction . It is the two-dimensional example of a horosphere (or orisphere).The centre of a horocycle is the ideal point where all normal geodesics asymptotically converge. Two horocycles who have the same centre are concentric.While it looks that two concentric horocycles cannot have the same length or curvature, in fact any two horocycles are congruent.A horocycle can also be described as the limit of the circles that share a tangent in a given point, as their radii go towards infinity. In Euclidean geometry, such a "circle of infinite radius" would be a straight line, but in hyperbolic geometry it is a horocycle (a curve) .From the convex side the horocycle is approximated by hypercycles whose distances from their axis go towards infinity.".
- Horocycle thumbnail Horocycle_normals.svg?width=300.
- Horocycle wikiPageExternalLink Stillwell%20J.%20The%20Four%20Pillars%20of%20Geometry(Springer,%202005)(239s)_MD_.pdfThe.
- Horocycle wikiPageID "11084460".
- Horocycle wikiPageLength "5527".
- Horocycle wikiPageOutDegree "36".
- Horocycle wikiPageRevisionID "683710282".
- Horocycle wikiPageWikiLink Apeirogon.
- Horocycle wikiPageWikiLink Category:Curves.
- Horocycle wikiPageWikiLink Category:Hyperbolic_geometry.
- Horocycle wikiPageWikiLink Compass-and-straightedge_construction.
- Horocycle wikiPageWikiLink Compass_and_straightedge_construction.
- Horocycle wikiPageWikiLink Concentric.
- Horocycle wikiPageWikiLink Congruence_(geometry).
- Horocycle wikiPageWikiLink E_(mathematical_constant).
- Horocycle wikiPageWikiLink Euclidean_geometry.
- Horocycle wikiPageWikiLink Gaussian_curvature.
- Horocycle wikiPageWikiLink Geodesic_curvature.
- Horocycle wikiPageWikiLink H._S._M._Coxeter.
- Horocycle wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Horocycle wikiPageWikiLink Horosphere.
- Horocycle wikiPageWikiLink Hyperbolic_geometry.
- Horocycle wikiPageWikiLink Hyperboloid_model.
- Horocycle wikiPageWikiLink Hypercycle_(geometry).
- Horocycle wikiPageWikiLink Hypercycle_(hyperbolic_geometry).
- Horocycle wikiPageWikiLink Ideal_point.
- Horocycle wikiPageWikiLink Infinity.
- Horocycle wikiPageWikiLink John_Wiley_&_Sons.
- Horocycle wikiPageWikiLink Limiting_parallel.
- Horocycle wikiPageWikiLink Normal_(geometry).
- Horocycle wikiPageWikiLink Perpendicular.
- Horocycle wikiPageWikiLink Poincaré_disk_model.
- Horocycle wikiPageWikiLink Poincaré_half-plane_model.
- Horocycle wikiPageWikiLink Special_cases_of_Apollonius_problem.
- Horocycle wikiPageWikiLink Tangent.
- Horocycle wikiPageWikiLink File:Apolleangasket_symmetry.png.
- Horocycle wikiPageWikiLink File:Horocycle_normals.svg.
- Horocycle wikiPageWikiLink File:Hyperbolic_apeirogon_example.png.
- Horocycle wikiPageWikiLink File:Order-3_apeirogonal_tiling_one_cell_horocycle.png.
- Horocycle wikiPageWikiLinkText "Horocycle".
- Horocycle wikiPageWikiLinkText "horocycle".
- Horocycle hasPhotoCollection Horocycle.
- Horocycle wikiPageUsesTemplate Template:Geometry-stub.
- Horocycle wikiPageUsesTemplate Template:Lang-el.
- Horocycle wikiPageUsesTemplate Template:Reflist.
- Horocycle subject Category:Curves.
- Horocycle subject Category:Hyperbolic_geometry.
- Horocycle hypernym Curve.
- Horocycle type Album.
- Horocycle type Article.
- Horocycle type Article.
- Horocycle type Surface.
- Horocycle comment "In hyperbolic geometry, a horocycle (Greek: ὅριον + κύκλος — border + circle, sometimes called an oricycle , oricircle, or limit circle ) is a curve whose normal or perpendicular geodesics all converge asymptotically in the same direction . It is the two-dimensional example of a horosphere (or orisphere).The centre of a horocycle is the ideal point where all normal geodesics asymptotically converge.".
- Horocycle label "Horocycle".
- Horocycle sameAs Horociclo.
- Horocycle sameAs Orociclo.
- Horocycle sameAs m.02q_h7g.
- Horocycle sameAs Орицикл.
- Horocycle sameAs Орицикл.
- Horocycle sameAs Q2246795.
- Horocycle sameAs Q2246795.
- Horocycle wasDerivedFrom Horocycle?oldid=683710282.
- Horocycle depiction Horocycle_normals.svg.
- Horocycle isPrimaryTopicOf Horocycle.