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Euler (1772ab) conjectured that there are no positive integer solutions to the quartic Diophantine equation A^4=B^4+C^4+D^4. This conjecture was disproved by Elkies (1988), ...

The Game of Logic, described by Lewis Carroll--author of Alice in Wonderland--in 1887 (Carroll 1972) consists of discussing the meaning of propositions like "Some fresh cakes ...

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 ...

A set-theoretic term having a number of different meanings. Fraenkel (1953, p. 37) used the term as a synonym for "finite set." However, according to Russell's definition ...

In statistical mechanics, the two-dimensional Ising model is a popular tool used to study the dipole moments of magnetic spins. The Ising model in two dimensions is a type of ...

The Jahangir graph J_(n,m) is a kind of generalized wheel graph with consisting of mn circular vertices and a central vertex connected to every mth vertex around the circle. ...

Multiple edges are two or more edges connecting the same two vertices within a multigraph. Multiple edges of degree d_(ij) between vertex i and vertex j correspond to an ...

There are at least 15 classes of convex pentagonal tilings, as illustrated above. The first five were discovered during investigations of German mathematician Karl Reinhardt ...

Petersen's theorem states that every cubic graph with no bridges has a perfect matching (Petersen 1891; Frink 1926; König 1936; Skiena 1990, p. 244). In fact, this theorem ...

A sequence of n-tuples that fills n-space more uniformly than uncorrelated random points, sometimes also called a low-discrepancy sequence. Although the ordinary uniform ...