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Given 2n-1 numbers a_k, where k=-n+1, ..., -1, 0, 1, ..., n-1, a Toeplitz matrix is a matrix which has constant values along negative-sloping diagonals, i.e., a matrix of the ...

The exact values of cos(pi/18) and sin(pi/18) can be given by infinite nested radicals sin(pi/(18))=1/2sqrt(2-sqrt(2+sqrt(2+sqrt(2-...)))), where the sequence of signs +, +, ...

Let V be a real symmetric matrix of large order N having random elements v_(ij) that for i<=j are independently distributed with equal densities, equal second moments m^2, ...

An invariant of an elliptic curve given in the form y^2=x^3+ax+b which is closely related to the elliptic discriminant and defined by j(E)=(2^83^3a^3)/(4a^3+27b^2). The ...

Klee's identity is the binomial sum sum_(k=0)^n(-1)^k(n; k)(n+k; m)=(-1)^n(n; m-n), where (n; k) is a binomial coefficient. For m=0, 1, ... and n=0, 1,..., the following ...

A tiling of regular polygons (in two dimensions), polyhedra (three dimensions), or polytopes (n dimensions) is called a tessellation. Tessellations can be specified using a ...

An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...

An algorithm which extrapolates the partial sums s_n of a series sum_(n)a_n whose convergence is approximately geometric and accelerates its rate of convergence. The ...

The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations. Analytic geometry ...

The Benney equation in 1+1 dimensions is the nonlinear partial differential equation ...