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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 wikiPageRevisionID "594134913".
- Five_points_determine_a_conic hasPhotoCollection Five_points_determine_a_conic.
- 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 Abstraction100002137.
- Five_points_determine_a_conic type Attribute100024264.
- Five_points_determine_a_conic type Communication100033020.
- Five_points_determine_a_conic type ConicSection113872975.
- Five_points_determine_a_conic type ConicSections.
- Five_points_determine_a_conic type Figure113862780.
- Five_points_determine_a_conic type Message106598915.
- Five_points_determine_a_conic type PlaneFigure113863186.
- Five_points_determine_a_conic type Proposition106750804.
- Five_points_determine_a_conic type Shape100027807.
- Five_points_determine_a_conic type Statement106722453.
- Five_points_determine_a_conic type Theorem106752293.
- Five_points_determine_a_conic type TheoremsInGeometry.
- 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".
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- Five_points_determine_a_conic sameAs Q5456251.
- Five_points_determine_a_conic sameAs Q5456251.
- Five_points_determine_a_conic sameAs Five_points_determine_a_conic.
- Five_points_determine_a_conic wasDerivedFrom Five_points_determine_a_conic?oldid=594134913.
- Five_points_determine_a_conic isPrimaryTopicOf Five_points_determine_a_conic.