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- Cramers_theorem_(algebraic_curves) abstract "In mathematics, Cramer's theorem on algebraic curves gives the necessary and sufficient number of points in the real plane falling on an algebraic curve to uniquely determine the curve in non-degenerate cases. This number is n(n + 3) / 2, where n is the degree of the curve. The theorem is due to Gabriel Cramer, who published it in 1750.For example, a line (of degree 1) is determined by 2 distinct points on it: only one line goes through those two points. Likewise, a non-degenerate conic (polynomial equation in x and y with the sum of their powers in any term not exceeding 2, hence with degree 2) is uniquely determined by 5 points in general position (no three of which are on a straight line).The intuition of the conic case is this: Suppose the given points fall on, specifically, an ellipse. Then five pieces of information are necessary and sufficient to identify the ellipse—the horizontal location of the ellipse's center, the vertical location of the center, the major axis (the length of the longest chord), the minor axis (the length of the shortest chord, perpendicular to the major axis), and the ellipse's rotational orientation (the extent to which the major axis departs from the horizontal). Five points in general position suffice to provide these five pieces of information, while four points do not.".
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- Cramers_theorem_(algebraic_curves) wikiPageRevisionID "650013282".
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Algebraic_curve.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Algebraic_equation.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Category:Algebra.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Category:Analytic_geometry.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Chord_(geometry).
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Circle.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Coefficient.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Cramers_paradox.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Degenerate_conic.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Degree_of_a_polynomial.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Determinant.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Determinant_(mathematics).
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Ellipse.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Five_points_determine_a_conic.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Gabriel_Cramer.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink General_position.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Major_axis.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Mathematics.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Minor_axis.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Necessary_and_sufficient.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Necessity_and_sufficiency.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Perpendicular.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Plane_(geometry).
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Plane_(mathematics).
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Polynomial_equation.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Radius.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Rotation_(mathematics).
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Semi-major_axis.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLink Semi-minor_axis.
- Cramers_theorem_(algebraic_curves) wikiPageWikiLinkText "Cramer's theorem (algebraic curves)".
- Cramers_theorem_(algebraic_curves) wikiPageWikiLinkText "Cramer's theorem (algebraic curves)#Restricted cases".
- Cramers_theorem_(algebraic_curves) wikiPageWikiLinkText "Cramer's theorem".
- Cramers_theorem_(algebraic_curves) hasPhotoCollection Cramers_theorem_(algebraic_curves).
- Cramers_theorem_(algebraic_curves) wikiPageUsesTemplate Template:Reflist.
- Cramers_theorem_(algebraic_curves) subject Category:Algebra.
- Cramers_theorem_(algebraic_curves) subject Category:Analytic_geometry.
- Cramers_theorem_(algebraic_curves) comment "In mathematics, Cramer's theorem on algebraic curves gives the necessary and sufficient number of points in the real plane falling on an algebraic curve to uniquely determine the curve in non-degenerate cases. This number is n(n + 3) / 2, where n is the degree of the curve. The theorem is due to Gabriel Cramer, who published it in 1750.For example, a line (of degree 1) is determined by 2 distinct points on it: only one line goes through those two points.".
- Cramers_theorem_(algebraic_curves) label "Cramer's theorem (algebraic curves)".
- Cramers_theorem_(algebraic_curves) sameAs m.012sddrn.
- Cramers_theorem_(algebraic_curves) sameAs Q20278711.
- Cramers_theorem_(algebraic_curves) sameAs Q20278711.
- Cramers_theorem_(algebraic_curves) wasDerivedFrom Cramers_theorem_(algebraic_curves)oldid=650013282.
- Cramers_theorem_(algebraic_curves) isPrimaryTopicOf Cramers_theorem_(algebraic_curves).