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The Zermelo-Fraenkel axioms are the basis for Zermelo-Fraenkel set theory. In the following (Jech 1997, p. 1), exists stands for exists, forall means for all, in stands for ...

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 Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...

In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the ...

Smarandache sequences are any of a number of simply generated integer sequences resembling those considered in published works by Smarandache such as the consecutive number ...

Let P be a finite partially ordered set, then an antichain in P is a set of pairwise incomparable elements. Antichains are also called Sperner systems in older literature ...

666 is the occult "number of the beast," also called the "sign of the devil" (Wang 1994), associated in the Bible with the Antichrist. It has figured in many numerological ...

The circumcircle is a triangle's circumscribed circle, i.e., the unique circle that passes through each of the triangle's three vertices. The center O of the circumcircle is ...

As a part of the study of Waring's problem, it is known that every positive integer is a sum of no more than 9 positive cubes (g(3)=9), that every "sufficiently large" ...