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An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually ...

The curlicue fractal is a figure obtained by the following procedure. Let s be an irrational number. Begin with a line segment of unit length, which makes an angle phi_0=0 to ...

Let O be an incidence geometry, i.e., a set with a symmetric, reflexive binary relation I. Let e and f be elements of O. Let an incidence plane be an incidence geometry whose ...

The Heawood graph is a cubic graph on 14 vertices and 21 edges which is the unique (3,6)-cage graph. It is also a Moore graph. It has graph diameter 3, graph radius 3, and ...

A planar graph G is said to be triangulated (also called maximal planar) if the addition of any edge to G results in a nonplanar graph. If the special cases of the triangle ...

The Tutte 8-cage (Godsil and Royle 2001, p. 59; right figure) is a cubic graph on 30 nodes and 45 edges which is the Levi graph of the Cremona-Richmond configuration. It ...

The Grassmannian Gr(n,k) is the set of k-dimensional subspaces in an n-dimensional vector space. For example, the set of lines Gr(n+1,1) is projective space. The real ...

A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on ...

A Hermitian inner product on a complex vector space V is a complex-valued bilinear form on V which is antilinear in the second slot, and is positive definite. That is, it ...

The Petersen graph is the cubic graph on 10 vertices and 15 edges which is the unique (3,5)-cage graph (Harary 1994, p. 175), as well as the unique (3,5)-Moore graph. It can ...