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Fermat's 4n+1 theorem, sometimes called Fermat's two-square theorem or simply "Fermat's theorem," states that a prime number p can be represented in an essentially unique ...

A giraffe graph is a graph formed by all possible moves of a hypothetical chess piece called a "giraffe" which moves analogously to a knight except that it is restricted to ...

The great dirhombicosidodecahedron is the uniform polyhedron with Maeder index 75 (Maeder 1997), Wenninger index 119 (Wenninger 1989), Coxeter index 82 (Coxeter et al. 1954), ...

A polygonal number and 6-polygonal number of the form n(2n-1). The first few are 1, 6, 15, 28, 45, ... (OEIS A000384). The generating function for the hexagonal numbers is ...

The m×n knight graph is a graph on mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a knight (which may ...

A Moiré pattern is an interference pattern produced by overlaying similar but slightly offset templates. A simple example is obtained by taking two identical ruled ...

A set n distinct numbers taken from the interval [1,n^2] form a magic series if their sum is the nth magic constant M_n=1/2n(n^2+1) (Kraitchik 1942, p. 143). If the sum of ...

A set of four points, one of which is the orthocenter of the other three. In an orthocentric system, each point is the orthocenter of the triangle of the other three, as ...

Hadamard matrices H_n can be constructed using finite field GF(p^m) when p=4l-1 and m is odd. Pick a representation r relatively prime to p. Then by coloring white ...

A linkage with six rods which draws the inverse of a given curve. When a pencil is placed at P, the inverse is drawn at P^' (or vice versa). If a seventh rod (dashed) is ...