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Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity. Two quantities A and B which are within ...

A simple unlabeled graph on n vertices is called pancyclic if it contains cycles of all lengths, 3, 4, ..., n. Since a pancyclic graph must contain a cycle of length n, ...

A function f(x) is said to be periodic (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period p if f(x)=f(x+np) for ...

For a permutation alpha in the symmetric group S_p, the alpha-permutation graph of a labeled graph G is the graph union of two disjoint copies of G (say, G_1 and G_2), ...

A permutation matrix is a matrix obtained by permuting the rows of an n×n identity matrix according to some permutation of the numbers 1 to n. Every row and column therefore ...

Given two intersecting lines OA and OB forming an angle with vertex at O and a point X inside the angle ∠AOB, the Philo line (or Philon line) is the shortest line segment AB ...

There exist polyhedra which can be plaited (braided). Examples include a plaited cube and plaited icosahedron illustrated above (Pargeter 1959, Wells 1991). In the above ...

A polyare is a polyform formed from a polyomino by removing of half of each square such that at least half of the original join between squares is retained. The first few ...

An n-he (a term coined by Brendan Owen) is a shape formed from a polyhex by removing half of each hexagon in such a way that the remaining pieces are connected (Clarke). The ...

Polykites are polyforms obtained from a regular triangular grid superposed on a regular hexagonal grid (its dual), illustrated above. The monokite is therefore a ...