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In mathematics, a quartic equation is one which can be expressed as a quartic function equaling zero. The general form of a quartic equation is The general form of a quartic equation is Graph of a polynomial function of degree 4, with its 4 roots and 3 critical points .
Each coordinate of the intersection points of two conic sections is a solution of a quartic equation. The same is true for the intersection of a line and a torus.It follows that quartic equations often arise in computational geometry and all related fields such as computer graphics, computer-aided design, computer-aided manufacturing and optics.
An explicit quartic with twenty-eight real bitangents was first given by Plücker [1] As Plücker showed, the number of real bitangents of any quartic must be 28, 16, or a number less than 9. Another quartic with 28 real bitangents can be formed by the locus of centers of ellipses with fixed axis lengths, tangent to two non-parallel lines. [2]
Quartic curve, an algebraic curve of degree 4; Quartic reciprocity, a theorem from number theory; Quartic surface, a surface defined by an equation of degree 4; See also. All pages with titles beginning with Quartic ; All pages with titles containing Quartic; Quart (disambiguation) Quintic, relating to degree 5, as next higher above quartic
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
The cruciform curve, or cross curve is a quartic plane curve given by the equation = where a and b are two parameters determining the shape of the curve. The cruciform curve is related by a standard quadratic transformation, x ↦ 1/x, y ↦ 1/y to the ellipse a 2 x 2 + b 2 y 2 = 1, and is therefore a rational plane algebraic curve of genus zero.
In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4. More specifically there are two closely related types of quartic surface: affine and projective.
The model belongs to the Griffiths-Simon class, [1] meaning that it can be represented also as the weak limit of an Ising model on a certain type of graph. The triviality of both the ϕ 4 {\displaystyle \phi ^{4}} model and the Ising model in d ≥ 4 {\displaystyle d\geq 4} can be shown via a graphical representation known as the random current ...