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- Algebraic_curve abstract "In mathematics, an algebraic curve or plane algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables. For example, the unit circle is an algebraic curve, being the set of zeros of the polynomial x2 + y2 − 1Various technical considerations have led to consider that the complex zeros of a polynomial belong to the curve. Also, the notion of algebraic curve has been generalized to allow the coefficients of the defining polynomial and the coordinates of the points of the curve to belong to any field, leading to the following definition.In algebraic geometry, a plane affine algebraic curve defined over a field k is the set of points of K2 whose coordinates are zeros of some bivariate polynomial with coefficients in k, where K is some algebraically closed extension of k. The points of the curve with coordinates in k are the k-points of the curve and, all together, are the k part of the curve.For example, is a point of the curve defined by x2 + y2 − 1 =0 and the usual unit circle is the real part of this curve. The term "unit circle" may refer to all the complex points as well to only the real points, the exact meaning being usually clear from the context. The equation x2 + y2 + 1 = 0 defines an algebraic curve, whose real part is empty.More generally, one may consider algebraic curves that are not contained in the plane, but in a space of higher dimension. A curve that is not contained in some plane is called a skew curve. The simplest example of a skew algebraic curve is the twisted cubic. One may also consider algebraic curves contained in the projective space and even algebraic curves that are defined independently to any embedding in an affine or projective space. This leads to the most general definition of an algebraic curve:In algebraic geometry, an algebraic curve is an algebraic variety of dimension one.".
- Algebraic_curve thumbnail Tschirnhausen_cubic.svg?width=300.
- Algebraic_curve wikiPageID "253260".
- Algebraic_curve wikiPageRevisionID "606759732".
- Algebraic_curve hasPhotoCollection Algebraic_curve.
- Algebraic_curve subject Category:Algebraic_curves.
- Algebraic_curve type Abstraction100002137.
- Algebraic_curve type AlgebraicCurves.
- Algebraic_curve type Attribute100024264.
- Algebraic_curve type Curve113867641.
- Algebraic_curve type Line113863771.
- Algebraic_curve type Shape100027807.
- Algebraic_curve comment "In mathematics, an algebraic curve or plane algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables. For example, the unit circle is an algebraic curve, being the set of zeros of the polynomial x2 + y2 − 1Various technical considerations have led to consider that the complex zeros of a polynomial belong to the curve.".
- Algebraic_curve label "Algebraic curve".
- Algebraic_curve label "Algebraische Kurve".
- Algebraic_curve label "Algebraïsche kromme".
- Algebraic_curve label "Courbe algébrique".
- Algebraic_curve label "Curva algebraica".
- Algebraic_curve label "Curva algébrica".
- Algebraic_curve label "Алгебраическая кривая".
- Algebraic_curve label "منحنى جبري".
- Algebraic_curve label "代数曲線".
- Algebraic_curve label "代數曲線".
- Algebraic_curve sameAs Algebraische_Kurve.
- Algebraic_curve sameAs Curva_algebraica.
- Algebraic_curve sameAs Courbe_algébrique.
- Algebraic_curve sameAs 代数曲線.
- Algebraic_curve sameAs 대수_곡선.
- Algebraic_curve sameAs Algebraïsche_kromme.
- Algebraic_curve sameAs Curva_algébrica.
- Algebraic_curve sameAs m.01lkwk.
- Algebraic_curve sameAs Q266237.
- Algebraic_curve sameAs Q266237.
- Algebraic_curve sameAs Algebraic_curve.
- Algebraic_curve wasDerivedFrom Algebraic_curve?oldid=606759732.
- Algebraic_curve depiction Tschirnhausen_cubic.svg.
- Algebraic_curve isPrimaryTopicOf Algebraic_curve.