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  2. Algebraic curve - Wikipedia

    en.wikipedia.org/wiki/Algebraic_curve

    An algebraic curve in the Euclidean plane is the set of the points whose coordinates are the solutions of a bivariate polynomial equation p(x, y) = 0.This equation is often called the implicit equation of the curve, in contrast to the curves that are the graph of a function defining explicitly y as a function of x.

  3. Gallery of curves - Wikipedia

    en.wikipedia.org/wiki/Gallery_of_curves

    1 Algebraic curves. ... Download as PDF; Printable version; ... This is a gallery of curves used in mathematics, by Wikipedia page. See also list ...

  4. Curve - Wikipedia

    en.wikipedia.org/wiki/Curve

    A space curve is a curve for which is at least three-dimensional; a skew curve is a space curve which lies in no plane. These definitions of plane, space and skew curves apply also to real algebraic curves , although the above definition of a curve does not apply (a real algebraic curve may be disconnected ).

  5. List of curves - Wikipedia

    en.wikipedia.org/wiki/List_of_curves

    1.1 Algebraic curves. ... Download as PDF; ... This is a list of Wikipedia articles about curves used in different fields: mathematics ...

  6. Real algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Real_algebraic_geometry

    Real algebra is the part of algebra which is relevant to real algebraic (and semialgebraic) geometry. It is mostly concerned with the study of ordered fields and ordered rings (in particular real closed fields ) and their applications to the study of positive polynomials and sums-of-squares of polynomials .

  7. Algebraic variety - Wikipedia

    en.wikipedia.org/wiki/Algebraic_variety

    The twisted cubic is a projective algebraic variety. Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in ...

  8. Scheme (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Scheme_(mathematics)

    In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x 2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers).

  9. Algebraic cycle - Wikipedia

    en.wikipedia.org/wiki/Algebraic_cycle

    In mathematics, an algebraic cycle on an algebraic variety V is a formal linear combination of subvarieties of V. These are the part of the algebraic topology of V that is directly accessible by algebraic methods. Understanding the algebraic cycles on a variety can give profound insights into the structure of the variety.

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