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When computing the sample variance s numerically, the mean must be computed before s^2 can be determined. This requires storing the set of sample values. However, it is ...

A simple polyhedron, also called a simplicial polyhedron, is a polyhedron that is topologically equivalent to a sphere (i.e., if it were inflated, it would produce a sphere) ...

A pathwise-connected domain is said to be simply connected (also called 1-connected) if any simple closed curve can be shrunk to a point continuously in the set. If the ...

The nth Suzanne set S_n is defined as the set of composite numbers x for which n|S(x) and n|S_p(x), where x = a_0+a_1(10^1)+...+a_d(10^d) (1) = p_1p_2...p_m, (2) and S(x) = ...

A triangle tiling is a tiling of the plane by identical triangles. Any triangle tiles the plane (Wells 1991, p. 208). The total number of triangles (including inverted ones) ...

The truncated triangular prism is an undecagon obtained by truncation of a triangular prism. It has 18 vertices, 27 edges, and 11 faces. As a canonical polyhedron with unit ...

Let B_n(r) be the n-dimensional closed ball of radius r>1 centered at the origin. A function which is defined on B(r) is called an extension to B(r) of a function f defined ...

Willans' formula is a prime-generating formula due to Willan (1964) that is defined as follows. Let F(j) = |_cos^2[pi((j-1)!+1)/j]_| (1) = {1 for j=1 or j prime; 0 otherwise ...

Given two starting numbers (a_1,a_2), the following table gives the unique sequences {a_i} that contain no three-term arithmetic progressions. Sloane sequence A003278 1, 2, ...

A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...