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If x_1<x_2<...<x_n denote the zeros of p_n(x), there exist real numbers lambda_1,lambda_2,...,lambda_n such that ...

A golden isozonohedron is a zonohedron all of whose faces are golden rhombi. There exist exactly five golden isozonohedra, as summarized in the following table. face count ...

There are two different statements, each separately known as the greatest common divisor theorem. 1. Given positive integers m and n, it is possible to choose integers x and ...

A symmetric block design (4n+3, 2n+1, n) which is equivalent to a Hadamard matrix of order 4n+4. It is conjectured that Hadamard designs exist for all integers n>0, but this ...

A Hilbert basis for the vector space of square summable sequences (a_n)=a_1, a_2, ... is given by the standard basis e_i, where e_i=delta_(in), with delta_(in) the Kronecker ...

Two topological spaces X and Y are homotopy equivalent if there exist continuous maps f:X->Y and g:Y->X, such that the composition f degreesg is homotopic to the identity ...

A linear transformation A:R^n->R^n is hyperbolic if none of its eigenvalues has modulus 1. This means that R^n can be written as a direct sum of two A-invariant subspaces E^s ...

The incenter I is the center of the incircle for a polygon or insphere for a polyhedron (when they exist). The corresponding radius of the incircle or insphere is known as ...

An incircle is an inscribed circle of a polygon, i.e., a circle that is tangent to each of the polygon's sides. The center I of the incircle is called the incenter, and the ...

The infimum is the greatest lower bound of a set S, defined as a quantity m such that no member of the set is less than m, but if epsilon is any positive quantity, however ...