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Given two circles, draw the tangents from the center of each circle to the sides of the other. Then the line segments AB and CD are of equal length. The theorem can be proved ...

A number of the form 2^n-1 obtained by setting x=1 in a Fermat-Lucas polynomial, more commonly known as a Mersenne number.

The ring of fractions of an integral domain. The field of fractions of the ring of integers Z is the rational field Q, and the field of fractions of the polynomial ring ...

A finite extension K=Q(z)(w) of the field Q(z) of rational functions in the indeterminate z, i.e., w is a root of a polynomial a_0+a_1alpha+a_2alpha^2+...+a_nalpha^n, where ...

Given two univariate polynomials of the same order whose first p coefficients (but not the first p-1) are 0 where the coefficients of the second approach the corresponding ...

The abscissas of the N-point Gaussian quadrature formula are precisely the roots of the orthogonal polynomial for the same interval and weighting function.

The solution to a game in game theory. When a game saddle point is present max_(i<=m)min_(j<=n)a_(ij)=min_(j<=n)max_(i<=m)a_(ij)=v, and v is the value for pure strategies.

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 ...

f(x) approx t_n(x)=sum_(k=0)^(2n)f_kzeta_k(x), where t_n(x) is a trigonometric polynomial of degree n such that t_n(x_k)=f_k for k=0, ..., 2n, and ...

The co-rank of a graph G is defined as s(G)=m-n+c, where m is the number of edges of G, n is the number of vertices, and c is the number of connected components (Biggs 1993, ...