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The summatory function Phi(n) of the totient function phi(n) is defined by Phi(n) = sum_(k=1)^(n)phi(k) (1) = sum_(m=1)^(n)msum_(d|m)(mu(d))/d (2) = ...

Euler's series transformation is a transformation that sometimes accelerates the rate of convergence for an alternating series. Given a convergent alternating series with sum ...

A vector difference is the result of subtracting one vector from another. A vector difference is denoted using the normal minus sign, i.e., the vector difference of vectors A ...

How can n points be distributed on a unit sphere such that they maximize the minimum distance between any pair of points? This maximum distance is called the covering radius, ...

A method for finding roots of a polynomial equation f(x)=0. Now find an equation whose roots are the roots of this equation diminished by r, so (1) The expressions for f(r), ...

Let |A| denote the cardinal number of set A, then it follows immediately that |A union B|=|A|+|B|-|A intersection B|, (1) where union denotes union, and intersection denotes ...

A bicentric quadrilateral, also called a cyclic-inscriptable quadrilateral, is a four-sided bicentric polygon. The inradius r, circumradius R, and offset x are connected by ...

Conway's soldiers, also known as the "solitaire army" game (Berlekamp et al. 1982) or "checker-jumping problem" (Honsberger 1976) is a one-player game played on an infinite ...

The minimum spanning tree of a weighted graph is a set of edges of minimum total weight which form a spanning tree of the graph. When a graph is unweighted, any spanning tree ...

There are a number of functions in various branches of mathematics known as Riemann functions. Examples include the Riemann P-series, Riemann-Siegel functions, Riemann theta ...