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A sequence produced by the instructions "reverse, add to the original, then sort the digits." For example, after 668, the next iteration is given by 668+866=1534, so the next ...

Somos's quadratic recurrence constant is defined via the sequence g_n=ng_(n-1)^2 (1) with g_0=1. This has closed-form solution ...

The Wiener-Hopf method is a powerful technique which enables certain linear partial differential equations subject to boundary conditions on semi-infinite domains to be ...

Number Theory

There are several commonly used methods of defining the slippery, but extremely important, concept of a continuous function (which, depending on context, may also be called a ...

The Johnson triangle DeltaJ_AJ_BJ_C, a term coined here for the first time, is the triangle formed by the centers of the Johnson circles. It has trilinear vertex matrix ...

A triangle line lalpha+mbeta+ngamma=0 defined relative to a reference triangle is called a central line iff l:m:n is a triangle center (Kimberling 1998, p. 127). If l:m:n is ...

The distance between two points is the length of the path connecting them. In the plane, the distance between points (x_1,y_1) and (x_2,y_2) is given by the Pythagorean ...

Calculus I

Given a triangle center X=l:m:n, the line mnalpha+nlbeta+lmgamma=0, where alpha:beta:gamma are trilinear coordinates, is called the trilinear polar (Kimberling 1998, p. 38). ...