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- Five_points_determine_a_conic abstract "In Euclidean, non-projective geometry, just as two (distinct) points determine a line (a degree-1 plane curve), five points determine a conic (a degree-2 plane curve). There are additional subtleties for conics that do not exist for lines, and thus the statement and its proof for conics are both more technical than for lines. In projective geometry, a line is defined via three points, all families of circles are conics passing through two points of a line at infinity, and coordinates are the basic conic objects of study, and are defined as all conics passing through the line and two points at infinity.Formally, given any five points in the plane in general linear position, meaning no three collinear, there is a unique conic passing through them, which will be non-degenerate; this is true over both the affine plane and projective plane. Indeed, given any five points there is a conic passing through them, but if three of the points are collinear the conic will be degenerate (reducible, because it contains a line), and may not be unique; see further discussion.".
- Five_points_determine_a_conic wikiPageExternalLink FivePointsDetermineAConicSection.
- Five_points_determine_a_conic wikiPageID "26269427".
- Five_points_determine_a_conic wikiPageLength "13162".
- Five_points_determine_a_conic wikiPageOutDegree "47".
- Five_points_determine_a_conic wikiPageRevisionID "690378944".
- Five_points_determine_a_conic wikiPageWikiLink Apollonian_circles.
- Five_points_determine_a_conic wikiPageWikiLink Base_locus.
- Five_points_determine_a_conic wikiPageWikiLink Binomial_coefficient.
- Five_points_determine_a_conic wikiPageWikiLink Braikenridge–Maclaurin_theorem.
- Five_points_determine_a_conic wikiPageWikiLink Bxc3xa9zouts_theorem.
- Five_points_determine_a_conic wikiPageWikiLink Category:Conic_sections.
- Five_points_determine_a_conic wikiPageWikiLink Category:Projective_geometry.
- Five_points_determine_a_conic wikiPageWikiLink Category:Theorems_in_geometry.
- Five_points_determine_a_conic wikiPageWikiLink Cayley–Bacharach_theorem.
- Five_points_determine_a_conic wikiPageWikiLink Circle.
- Five_points_determine_a_conic wikiPageWikiLink Codimension.
- Five_points_determine_a_conic wikiPageWikiLink Collinearity.
- Five_points_determine_a_conic wikiPageWikiLink Conic_section.
- Five_points_determine_a_conic wikiPageWikiLink Cramers_theorem_(algebraic_curves).
- Five_points_determine_a_conic wikiPageWikiLink Degenerate_conic.
- Five_points_determine_a_conic wikiPageWikiLink Duality_(projective_geometry).
- Five_points_determine_a_conic wikiPageWikiLink Enumerative_geometry.
- Five_points_determine_a_conic wikiPageWikiLink General_position.
- Five_points_determine_a_conic wikiPageWikiLink Geometry.
- Five_points_determine_a_conic wikiPageWikiLink Group_action.
- Five_points_determine_a_conic wikiPageWikiLink Hypersurface.
- Five_points_determine_a_conic wikiPageWikiLink Jakob_Steiner.
- Five_points_determine_a_conic wikiPageWikiLink Line_(geometry).
- Five_points_determine_a_conic wikiPageWikiLink Linear_algebra.
- Five_points_determine_a_conic wikiPageWikiLink Linear_system_of_divisors.
- Five_points_determine_a_conic wikiPageWikiLink Mathematical_Association_of_America.
- Five_points_determine_a_conic wikiPageWikiLink Morphism_of_algebraic_varieties.
- Five_points_determine_a_conic wikiPageWikiLink Multiset.
- Five_points_determine_a_conic wikiPageWikiLink Pascals_theorem.
- Five_points_determine_a_conic wikiPageWikiLink Pencil_(mathematics).
- Five_points_determine_a_conic wikiPageWikiLink Pigeonhole_principle.
- Five_points_determine_a_conic wikiPageWikiLink Pochhammer_symbol.
- Five_points_determine_a_conic wikiPageWikiLink Problem_of_Apollonius.
- Five_points_determine_a_conic wikiPageWikiLink Projective_geometry.
- Five_points_determine_a_conic wikiPageWikiLink Projective_plane.
- Five_points_determine_a_conic wikiPageWikiLink Synthetic_geometry.
- Five_points_determine_a_conic wikiPageWikiLink Two-dimensional_space.
- Five_points_determine_a_conic wikiPageWikiLink Veronese_surface.
- Five_points_determine_a_conic wikiPageWikiLink File:Apollonian_circles.svg.
- Five_points_determine_a_conic wikiPageWikiLink File:Parabola_construction_given_five_points.gif.
- Five_points_determine_a_conic wikiPageWikiLinkText "Five points determine a conic".
- Five_points_determine_a_conic wikiPageWikiLinkText "Five points determine a conic#Braikenridge–Maclaurin construction".
- Five_points_determine_a_conic wikiPageWikiLinkText "defined by five points".
- Five_points_determine_a_conic wikiPageWikiLinkText "five points determine a conic".
- Five_points_determine_a_conic wikiPageWikiLinkText "five points".
- Five_points_determine_a_conic wikiPageUsesTemplate Template:Citation.
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- Five_points_determine_a_conic subject Category:Conic_sections.
- Five_points_determine_a_conic subject Category:Projective_geometry.
- Five_points_determine_a_conic subject Category:Theorems_in_geometry.
- Five_points_determine_a_conic type Redirect.
- Five_points_determine_a_conic type Theorem.
- Five_points_determine_a_conic comment "In Euclidean, non-projective geometry, just as two (distinct) points determine a line (a degree-1 plane curve), five points determine a conic (a degree-2 plane curve). There are additional subtleties for conics that do not exist for lines, and thus the statement and its proof for conics are both more technical than for lines.".
- Five_points_determine_a_conic label "Five points determine a conic".
- Five_points_determine_a_conic sameAs Q5456251.
- Five_points_determine_a_conic sameAs m.0b764p8.
- Five_points_determine_a_conic sameAs Q5456251.
- Five_points_determine_a_conic wasDerivedFrom Five_points_determine_a_conic?oldid=690378944.
- Five_points_determine_a_conic isPrimaryTopicOf Five_points_determine_a_conic.