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There are a number of attractive polyhedron compounds consisting of five cubes. The first of these (left figures) consists of the arrangement of five cubes in the polyhedron ...

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices ...

The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

The word "algebra" is a distortion of the Arabic title of a treatise by al-Khwārizmī about algebraic methods. In modern usage, algebra has several meanings. One use of the ...

A Gröbner basis G for a system of polynomials A is an equivalence system that possesses useful properties, for example, that another polynomial f is a combination of those in ...

A sphere is defined as the set of all points in three-dimensional Euclidean space R^3 that are located at a distance r (the "radius") from a given point (the "center"). Twice ...

"Chaos" is a tricky thing to define. In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. ...

Closed forms are known for the sums of reciprocals of even-indexed Fibonacci numbers P_F^((e)) = sum_(n=1)^(infty)1/(F_(2n)) (1) = ...

Theodorus's constant sqrt(3) has decimal expansion sqrt(3)=1.732050807... (OEIS A002194). It was computed to 10^(10) decimal digits by E. Weisstein on Jul. 23, 2013. The ...

For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...