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Kloosterman's sum is defined by S(u,v,n)=sum_(h)exp[(2pii(uh+vh^_))/n], (1) where h runs through a complete set of residues relatively prime to n and h^_ is defined by hh^_=1 ...

The Lucas central triangle (a term coined here for the first time) is the triangle DeltaL_AL_BL_C formed by the centers of the Lucas circles of a given reference triangle ...

The MacBeath inconic of a triangle is the inconic with parameters x:y:z=a^2cosA:b^2cosB:c^2cosC. (1) Its foci are the circumcenter O and the orthocenter H, giving the center ...

The power series that defines the exponential map e^x also defines a map between matrices. In particular, exp(A) = e^(A) (1) = sum_(n=0)^(infty)(A^n)/(n!) (2) = ...

Given a square complex or real matrix A, a matrix norm ||A|| is a nonnegative number associated with A having the properties 1. ||A||>0 when A!=0 and ||A||=0 iff A=0, 2. ...

If two points A and A^' are inverse (sometimes called conjugate) with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to ...

Rule 50 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

Let psi_1(x) and psi_2(x) be any two real integrable functions in [a,b], then Schwarz's inequality is given by |<psi_1|psi_2>|^2<=<psi_1|psi_1><psi_2|psi_2>. (1) Written out ...

A secant line, also simply called a secant, is a line passing through two points of a curve. As the two points are brought together (or, more precisely, as one is brought ...

There are two types of singular values, one in the context of elliptic integrals, and the other in linear algebra. For a square matrix A, the square roots of the eigenvalues ...