quartic curve

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• Quartic plane curve — A quartic plane curve is a plane curve of the fourth degree. It can be defined by a quartic equation::Ax^4+By^4+Cx^3y+Dx^2y^2+Exy^3+Fx^3+Gy^3+Hx^2y+Ixy^2+Jx^2+Ky^2+Lxy+Mx+Ny+P=0.This equation has fifteen constants. However, it can be multiplied… …   Wikipedia

• Quartic — Quar tic, n. (a) (Alg.) A quantic of the fourth degree. See {Quantic}. (b) (Geom.) A curve or surface whose equation is of the fourth degree in the variables. [1913 Webster] …   The Collaborative International Dictionary of English

• quartic — [ kwɔ:tɪk] adjective Mathematics denoting an equation, curve, etc. involving the fourth and no higher power of an unknown quantity or variable. Origin C19: from L. quartus fourth + ic …   English new terms dictionary

• Klein quartic — In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus 3 with the highest possible order automorphism group for this genus, namely order 168. As such, the Klein quartic is the Hurwitz surface of… …   Wikipedia

• Algebraic curve — In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with… …   Wikipedia

• Bullet-nose curve — In mathematics, a bullet nose curve is a unicursal quartic curve with three inflection points, given by the equation:a^2y^2 b^2x^2=x^2y^2 ,The bullet curve has three double points in the real projective plane, at x=0 and y=0, x=0 and z=0, and y=0 …   Wikipedia

• Bézier curve — Cubic Bézier curve A Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case. In… …   Wikipedia

• Trott curve — In real algebraic geometry, the Trott curve is the set of points ( x , y ) satisfying the degree four polynomial equation:displaystyle 144(x^4+y^4) 225(x^2+y^2)+350x^2y^2+81=0.These points form a nonsingular quartic plane curve that has genus… …   Wikipedia

• Plane curve — In mathematics, a plane curve is a curve in a Euclidean plane (cf. space curve). The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. A smooth plane curve is a curve in a …   Wikipedia

• Modular curve — In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half plane H by the action of a congruence subgroup Γ of the modular group of …   Wikipedia

• Hyperelliptic curve — In algebraic geometry, a hyperelliptic curve (over the complex numbers) is an algebraic curve given by an equation of the form:y^2 = f(x)where f(x) is a polynomial of degree n > 4 with n distinct roots. A hyperelliptic function is a function from …   Wikipedia