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The regular octagon is the regular polygon with eight sides, as illustrated above. The inradius r, circumradius R, and area A of the regular octagon can be computed directly ...

For a set partition of n elements, the n-character string a_1a_2...a_n in which each character gives the set block (B_0, B_1, ...) in which the corresponding element belongs ...

The Ricci curvature tensor, also simply known as the Ricci tensor (Parker and Christensen 1994), is defined by R_(mukappa)=R^lambda_(mulambdakappa), where ...

The root separation (or zero separation) of a polynomial P(x) with roots r_1, r_2, ... is defined by Delta(P)=min_(i!=j)|r_i-r_j|. There are lower bounds on how close two ...

There exists a positive integer s such that every sufficiently large integer is the sum of at most s primes. It follows that there exists a positive integer s_0>=s such that ...

If P(n) is a sentential formula depending on a variable n ranging in a set of real numbers, the sentence P(n) for every sufficiently large n (1) means exists N such that P(n) ...

Tomography is the study of the reconstruction of two- and three-dimensional objects from one-dimensional slices. The Radon transform is an important tool in tomography. ...

Let gamma(G) denote the domination number of a simple graph G. Then Vizing (1963) conjectured that gamma(G)gamma(H)<=gamma(G×H), where G×H is the graph product. While the ...

Let points A^', B^', and C^' be marked off some fixed distance x along each of the sides BC, CA, and AB. Then the lines AA^', BB^', and CC^' concur in a point U known as the ...

The de Bruijn constant, also called the Copson-de Bruijn constant, is the minimal constant c=1.1064957714... (OEIS A113276) such that the inequality ...