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A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

A plane-filling arrangement of plane figures or its generalization to higher dimensions. Formally, a tiling is a collection of disjoint open sets, the closures of which cover ...

Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

Let p be a prime with n digits and let A be a constant. Call p an "A-prime" if the concatenation of the first n digits of A (ignoring the decimal point if one is present) ...

A finite group is a group having finite group order. Examples of finite groups are the modulo multiplication groups, point groups, cyclic groups, dihedral groups, symmetric ...

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not ...

Given a "good" graph G (i.e., one for which all intersecting graph edges intersect in a single point and arise from four distinct graph vertices), the crossing number is the ...

A random number is a number chosen as if by chance from some specified distribution such that selection of a large set of these numbers reproduces the underlying ...

In the field of percolation theory, the term percolation threshold is used to denote the probability which "marks the arrival" (Grimmett 1999) of an infinite connected ...