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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.
Algebraic curves. Rational curves. Rational curves are subdivided according to the degree of the polynomial. Degree 1. Line; Degree 2. Plane curves ...
Algebraic curves in the plane may be defined as the set of points (x, y) satisfying an equation of the form (,) =, where f is a polynomial function :. If f is expanded as = + + + + + + If the origin (0, 0) is on the curve then a 0 = 0.
In the common case of a real algebraic curve, where k is the field of real numbers, an algebraic curve is a finite union of topological curves. When complex zeros are considered, one has a complex algebraic curve, which, from the topological point of view, is not a curve, but a surface, and is often called a Riemann surface. Although not being ...
Algebraic varieties of dimension one are called algebraic curves and algebraic varieties of dimension two are called algebraic surfaces. In the context of modern scheme theory, an algebraic variety over a field is an integral (irreducible and reduced) scheme over that field whose structure morphism is separated and of finite type.
Algebraic Curves ¿ Curves ¿ Curves: Cubic Plane Curve: Quartic Plane Curve: Rational Curves: Degree 2: Conic Section(s) Unit Circle: Unit Hyperbola: Degree 3: Folium of Descartes: Cissoid of Diocles: Conchoid of de Sluze: Right Strophoid: Semicubical Parabola: Serpentine Curve: Trident Curve: Trisectrix of Maclaurin: Tschirnhausen Cubic ...
This page was last edited on 18 January 2023, at 14:32 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
A Hurwitz curve is a complex algebraic curve of genus g>0 with the maximum possible number 84(g–1) of automorphisms. hyperbolism Essentially a blow-up of a curve at a point. See Salmon (1879, p.175). hypercusp A singularity of a curve of some multiplicity r whose tangent cone is a single line meeting the curve with order r+1. (Coolidge 1931 ...
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