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The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (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 maps a number to its cube. It is an odd function, as
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.
5-cube, Rectified 5-cube, 5-cube, Truncated 5-cube, Cantellated 5-cube, Runcinated 5-cube, Stericated 5-cube; 5-orthoplex, Rectified 5-orthoplex, Truncated 5-orthoplex, Cantellated 5-orthoplex, Runcinated 5-orthoplex; Prismatic uniform 5-polytope For each polytope of dimension n, there is a prism of dimension n+1. [citation needed]
The post 30 Math Puzzles (with Answers) to Test Your Smarts appeared first on Reader's Digest. ... Number cube. Math puzzle. Which number should replace the question mark? Answer: 9. Go figure.
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.
In graph theory, the hypercube graph Q n is the graph formed from the vertices and edges of an n-dimensional hypercube.For instance, the cube graph Q 3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube.
A cube has all multiplicities divisible by 3 (it is of the form a 3 for some a). The first: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728 (sequence A000578 in the OEIS). A perfect power has a common divisor m > 1 for all multiplicities (it is of the form a m for some a > 1 and m > 1).
The cube can be represented as the cell, and examples of a honeycomb are cubic honeycomb, order-5 cubic honeycomb, order-6 cubic honeycomb, and order-7 cubic honeycomb. [47] The cube can be constructed with six square pyramids, tiling space by attaching their apices. [48] Polycube is a polyhedron in which the faces of many cubes are attached.
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