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Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...

A base-b BBP-type formula is a convergent series formula of the type alpha=sum_(k=0)^infty(p(k))/(b^kq(k)) (1) where p(k) and q(k) are integer polynomials in k (Bailey 2000; ...

The conjugate gradient method is not suitable for nonsymmetric systems because the residual vectors cannot be made orthogonal with short recurrences, as proved in Voevodin ...

How far can a stack of n books protrude over the edge of a table without the stack falling over? It turns out that the maximum overhang possible d_n for n books (in terms of ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 or m=2,3, but only a small ...

Let there be n>=2 integers 0<a_1<...<a_n with GCD(a_1,a_2,...,a_n)=1. The values a_i represent the denominations of n different coins, where these denominations have greatest ...

A complete bipartite graph, sometimes also called a complete bicolored graph (Erdős et al. 1965) or complete bigraph, is a bipartite graph (i.e., a set of graph vertices ...

The convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S. For N points p_1, ..., p_N, the convex hull C is then given by the ...

If a, b, c, and d are points in the extended complex plane C^*, their cross ratio, also called the cross-ratio (Courant and Robbins 1996, p. 172; Durell 1928, p. 73), ...

The cube-connected cycle graph of order n is the graph obtained by replacing each vertex in a n-dimensional hypercube by a cycle of length n. They were introduced by ...