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Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis at y = 0).The case shown has two critical points.Here the function is () = (+) = (+) (+) and therefore the three real roots are 2, −1 and −4.
The graph of a cubic function always has a single inflection point. It may have two critical points, a local minimum and a local maximum. Otherwise, a cubic function is monotonic. The graph of a cubic function is symmetric with respect to its inflection point; that is, it is invariant under a rotation of a half turn around this point.
The Petersen graph is a cubic graph. The complete bipartite graph, is an example of a bicubic graph. In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs.
The vector [d 0, d 1, ..., d p−1] of the p integers is a suitable, although not unique, representation of the cubic Hamiltonian graph. This is augmented by two additional rules: If a d i > p/2, replace it by d i − p; avoid repetition of a sequence of d i if these are periodic and replace them by an exponential notation.
In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation F ( x , y , z ) = 0 {\displaystyle F(x,y,z)=0} applied to homogeneous coordinates ( x : y : z ) {\displaystyle (x:y:z)} for the projective plane ; or the inhomogeneous version for the affine space determined by setting z = 1 in such an ...
Two Dimensional Curves; Visual Dictionary of Special Plane Curves; Curves and Surfaces Index (Harvey Mudd College) National Curve Bank; An elementary treatise on cubic and quartic curves by Alfred Barnard Basset (1901) online at Google Books
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.
The cube of a number n is denoted n 3, using a superscript 3, [a] for example 2 3 = 8. The cube operation can also be defined for any other mathematical expression, for example (x + 1) 3. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n. The cube function is the function x ↦ x 3 (often denoted y = x 3) that ...