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The four roots x 1, x 2, x 3, and x 4 for the general quartic equation a x 4 + b x 3 + c x 2 + d x + e = 0 {\displaystyle ax^{4}+bx^{3}+cx^{2}+dx+e=0\,} with a ≠ 0 are given in the following formula, which is deduced from the one in the section on Ferrari's method by back changing the variables (see § Converting to a depressed quartic ) and ...
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 a pair of dual plane graphs or multigraphs. [5]
A drawing of a graph with 6 vertices and 7 edges. In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines).
Apollonian gasket; Apollonian sphere packing; Blancmange curve; Cantor dust; Cantor set; Cantor tesseract [citation needed]; Circle inversion fractal; De Rham curve; Douady rabbit; Dragon curve
Hemihelix, a quasi-helical shape characterized by multiple tendril perversions Tendril perversion (a transition between back-to-back helices) Seiffert's spiral [4]
For example, a circle of radius 2, centered at the origin of the plane, may be described as the set of all points whose coordinates x and y satisfy the equation x 2 + y 2 = 4; the area, the perimeter and the tangent line at any point can be computed from this equation by using integrals and derivatives, in a way that can be applied to any curve.
In the theory of quadratic forms, the parabola is the graph of the quadratic form x 2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x 2 + y 2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x 2 − y 2. Generalizations to more variables yield ...
The web graph W 4,2 is a cube. The web graph W n,r is a graph consisting of r concentric copies of the cycle graph C n, with corresponding vertices connected by "spokes". Thus W n,1 is the same graph as C n, and W n,2 is a prism. A web graph has also been defined as a prism graph Y n+1, 3, with the edges of the outer cycle removed. [7] [10]