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- Cramers_paradox abstract "In mathematics, Cramer's paradox or the Cramer–Euler paradox is the statement that the number of points of intersection of two higher-order curves in the plane can be greater than the number of arbitrary points that are usually needed to define one such curve. It is named after the Swiss mathematician Gabriel Cramer.This paradox is the result of a naive understanding or a misapplication of two theorems: Bézout's theorem (the number of points of intersection of two algebraic curves is equal to the product of their degrees, provided that certain necessary conditions are met). Cramer's theorem (a curve of degree n is determined by n(n + 3)/2 points, again assuming that certain conditions hold).Observe that for all n ≥ 3, n2 ≥ n(n + 3)/2, so it would naively appear that for degree three or higher there could be enough points shared by each of two curves that those points should determine either of the curves uniquely.The resolution of the paradox is that in certain degenerate cases n(n + 3) / 2 points are not enough to determine a curve uniquely.".
- Cramers_paradox thumbnail Two_cubic_curves.png?width=300.
- Cramers_paradox wikiPageExternalLink HEDI-2004-08.pdf.
- Cramers_paradox wikiPageExternalLink kmath207.htm.
- Cramers_paradox wikiPageID "22637653".
- Cramers_paradox wikiPageLength "5209".
- Cramers_paradox wikiPageOutDegree "16".
- Cramers_paradox wikiPageRevisionID "679306261".
- Cramers_paradox wikiPageWikiLink Algebraic_curve.
- Cramers_paradox wikiPageWikiLink Bxc3xa9zouts_theorem.
- Cramers_paradox wikiPageWikiLink Category:Algebraic_curves.
- Cramers_paradox wikiPageWikiLink Category:Algebraic_geometry.
- Cramers_paradox wikiPageWikiLink Category:Mathematics_paradoxes.
- Cramers_paradox wikiPageWikiLink Colin_Maclaurin.
- Cramers_paradox wikiPageWikiLink Cramers_theorem_(algebraic_curves).
- Cramers_paradox wikiPageWikiLink Gabriel_Cramer.
- Cramers_paradox wikiPageWikiLink Introductio_in_analysin_infinitorum.
- Cramers_paradox wikiPageWikiLink James_Stirling_(mathematician).
- Cramers_paradox wikiPageWikiLink Julius_Plücker.
- Cramers_paradox wikiPageWikiLink Leonhard_Euler.
- Cramers_paradox wikiPageWikiLink Line_(geometry).
- Cramers_paradox wikiPageWikiLink Mathematics.
- Cramers_paradox wikiPageWikiLink Plane_(geometry).
- Cramers_paradox wikiPageWikiLink File:Two_cubic_curves.png.
- Cramers_paradox wikiPageWikiLinkText "Cramer's paradox".
- Cramers_paradox wikiPageUsesTemplate Template:Reflist.
- Cramers_paradox subject Category:Algebraic_curves.
- Cramers_paradox subject Category:Algebraic_geometry.
- Cramers_paradox subject Category:Mathematics_paradoxes.
- Cramers_paradox hypernym Statement.
- Cramers_paradox type Variety.
- Cramers_paradox comment "In mathematics, Cramer's paradox or the Cramer–Euler paradox is the statement that the number of points of intersection of two higher-order curves in the plane can be greater than the number of arbitrary points that are usually needed to define one such curve.".
- Cramers_paradox label "Cramer's paradox".
- Cramers_paradox sameAs Q3363319.
- Cramers_paradox sameAs Paradoxe_de_Cramer.
- Cramers_paradox sameAs クラメールのパラドックス.
- Cramers_paradox sameAs m.05zxjdm.
- Cramers_paradox sameAs Q3363319.
- Cramers_paradox wasDerivedFrom Cramers_paradox?oldid=679306261.
- Cramers_paradox depiction Two_cubic_curves.png.
- Cramers_paradox isPrimaryTopicOf Cramers_paradox.