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The graph of any cubic function is similar to such a curve. The graph of a cubic function is a cubic curve, though many cubic curves are not graphs of functions. Although cubic functions depend on four parameters, their graph can have only very few shapes. In fact, the graph of a cubic function is always similar to the graph of a function of ...
The discriminant Δ of the cubic is the square of = () (), where a is the leading coefficient of the cubic, and r 1, r 2 and r 3 are the three roots of the cubic. As Δ {\displaystyle {\sqrt {\Delta }}} changes of sign if two roots are exchanged, Δ {\displaystyle {\sqrt {\Delta }}} is fixed by the Galois group only if the Galois group is A 3 .
1.1 Draw a segment of a cubic function exactly using a cubic Bezier curve. 6 comments. ... Is it possible to draw a segment of a cubic curve exactly with one ...
The number of connected simple cubic graphs on 4, 6, 8, 10, ... vertices is 1, 2, 5, 19, ... (sequence A002851 in the OEIS). A classification according to edge connectivity is made as follows: the 1-connected and 2-connected graphs are defined as usual. This leaves the other graphs in the 3-connected class because each 3-regular graph can be ...
Cubic Bézier curve with four control points The basis functions on the range t in [0,1] for cubic Bézier curves: blue: y = (1 − t) 3, green: y = 3(1 − t) 2 t, red: y = 3(1 − t)t 2, and cyan: y = t 3. A Bézier curve (/ ˈ b ɛ z. i. eɪ / BEH-zee-ay, [1] French pronunciation:) is a parametric curve used in computer graphics and related ...
The vertical scale is compressed 1:50 relative to the horizontal scale for ease of viewing. Thanks to Álvaro Lozano-Robledo for a method to find a cubic function with distinct special points with non-zero integer coordinates.
According to Brooks' theorem every connected cubic graph other than the complete graph K 4 has a vertex coloring with at most three colors. Therefore, every connected cubic graph other than K 4 has an independent set of at least n/3 vertices, where n is the number of vertices in the graph: for instance, the largest color class in a 3-coloring has at least this many vertices.
The 1st equal areas cubic is the locus of a point X such that area of the cevian triangle of X equals the area of the cevian triangle of X*. Also, this cubic is the locus of X for which X* is on the line S*X, where S is the Steiner point. (S = X(99) in the Encyclopedia of Triangle Centers).