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The rascal triangle is a number triangle with numbers arranged in staggered rows such that a_(n,r)=n(r-n)+1. (1) The published study of this triangle seems to have originated ...

In analysis, the phrase "Riesz-Fischer theorem" is used to describe a number of results concerning the convergence of Cauchy sequences in L-p spaces. The theorem is named for ...

Set covering deployment (sometimes written "set-covering deployment" and abbreviated SCDP for "set covering deployment problem") seeks an optimal stationing of troops in a ...

The number of cells in a generalized Chinese checkers board (or "centered" hexagram). Unlike the polygonal numbers, there is ambiguity in the case of the star numbers as to ...

A unigraphic graph (or simply a "unigraph") is a graph that is isomorphic to every graph having that degree sequence. All graphs on four are fewer vertices are unigraphic. ...

A number v=xy with an even number n of digits formed by multiplying a pair of n/2-digit numbers (where the digits are taken from the original number in any order) x and y ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...

The important binomial theorem states that sum_(k=0)^n(n; k)r^k=(1+r)^n. (1) Consider sums of powers of binomial coefficients a_n^((r)) = sum_(k=0)^(n)(n; k)^r (2) = ...

The absolute value of a real number x is denoted |x| and defined as the "unsigned" portion of x, |x| = xsgn(x) (1) = {-x for x<=0; x for x>=0, (2) where sgn(x) is the sign ...

The alternating factorial is defined as the sum of consecutive factorials with alternating signs, a(n)=sum_(k=1)^n(-1)^(n-k)k!. (1) They can be given in closed form as ...