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A perfect magic cube is a magic cube for which the rows, columns, pillars, space diagonals, and diagonals of each n×n orthogonal slice sum to the same number (i.e., the magic ...

The rectilinear crossing number of a graph G is the minimum number of crossings in a straight line embedding of G in a plane. It is variously denoted rcr(G), cr^_(G) ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ = (13)/(720)-(pi^2)/(15015) (1) = ...

The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric ...

"Abstract nonsense" is a nonderogatory term that is commonly used by mathematicians when skipping over parts of an argument that can be proven through a commonly used long ...

A gambling game played at carnivals in which a player may bet on any one of the numbers 1 through 6. Three dice are then rolled and, if his number appears, he receives back a ...

A set of ascending sequences in a permutation is called a run (Graham et al. 1994) or sometimes a rise (Comtet 1974, p. 241). A sorted permutation consists of a single run, ...

The solid angle Omega subtended by a surface S is defined as the surface area Omega of a unit sphere covered by the surface's projection onto the sphere. This can be written ...

A random matrix is a matrix of given type and size whose entries consist of random numbers from some specified distribution. Random matrix theory is cited as one of the ...