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The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

Every polynomial equation having complex coefficients and degree >=1 has at least one complex root. This theorem was first proven by Gauss. It is equivalent to the statement ...

A root of a polynomial P(z) is a number z_i such that P(z_i)=0. The fundamental theorem of algebra states that a polynomial P(z) of degree n has n roots, some of which may be ...

A generalization of a solid such as a cube or a sphere to more than three dimensions. A four-dimensional version of a polyhedron is known as a polytope.

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the local discrepancy is defined as D(J,P)=|(number of x_n in J)/N-Vol(J)|, Vol(J) is the ...

There are a number of attractive polyhedron compounds consisting of six octahedra. The two illustrated above can be constructed as the duals of cube 6-compounds. These ...

There are a number of attractive polyhedron compounds consisting of nine octahedra. The compound illustrated above can be constructed as the dual of cube 9-compound. The ...

A configuration of 12 planes and 12 points such that six points lie in every plane and six planes pass through every point. Alternatively, the configuration consists of 16 ...

There are several different kinds of magic numbers. The digital root and magic constant are sometimes known as magic numbers. In baseball, the magic number for a team in ...

A cubic lattice is a lattice whose points lie at positions (x,y,z) in the Cartesian three-space, where x, y, and z are integers. The term is also used to refer to a regular ...