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A quartic equation, or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form. where a ≠ 0. [1] The derivative of a quartic function is a cubic function. Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to a quadratic function of a square (or ...
The Folkman graph, a quartic graph with 20 vertices, the smallest semi-symmetric graph. [3] The Meredith graph, a quartic graph with 70 vertices that is 4-connected but has no Hamiltonian cycle, disproving a conjecture of Crispin Nash-Williams. [4] Every medial graph is a quartic plane graph, and every quartic plane graph is the medial graph of ...
The general form of a quartic equation is. Graph of a polynomial function of degree 4, with its 4 roots and 3 critical points. where a ≠ 0. The quartic is the highest order polynomial equation that can be solved by radicals in the general case (i.e., one in which the coefficients can take any value).
Klein quartic. (14-gon edges marked with the same number are equal.) The Klein quartic is a quotient of the heptagonal tiling (compare the 3-regular graph in green) and its dual triangular tiling (compare the 7-regular graph in violet). In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus 3 ...
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.
The graph of a cuboctahedron. The skeleton of a cuboctahedron may be represented as the graph, one of the Archimedean graph. It has 12 vertices and 24 edges. It is quartic graph, which is four vertices connecting each vertex. [20] The graph of a cuboctahedron may be constructed as the line graph of the cube, making it becomes the locally linear ...
In statistics, especially in Bayesian statistics, the kernel of a probability density function (pdf) or probability mass function (pmf) is the form of the pdf or pmf in which any factors that are not functions of any of the variables in the domain are omitted. [1] Note that such factors may well be functions of the parameters of the pdf or pmf.
Lamé's special quartic, named after Gabriel Lamé, is the graph of the equation. where . [1] It looks like a rounded square with "sides" of length and centered on the origin. This curve is a squircle centered on the origin, and it is a special case of a superellipse. [2] Because of Pierre de Fermat 's only surviving proof, that of the n = 4 ...