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A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i ...

An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in K. A nonsingular algebraic curve is an algebraic curve ...

A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...

The Celmins-Swart snarks are the two snarks on 26 vertices and 39 edges illustrated above. They are implemented in the Wolfram Language as GraphData["CelminsSwartSnark1"] and ...

A figurate number, also (but mostly in texts from the 1500 and 1600s) known as a figural number (Simpson and Weiner 1992, p. 587), is a number that can be represented by a ...

The gyroid, illustrated above, is an infinitely connected periodic minimal surface containing no straight lines (Osserman 1986) that was discovered by Schoen (1970). ...

A hex number, also called a centered hexagonal number, is given by H_n = 1+6T_n (1) = 3n^2+3n+1, (2) where T_n=n(n+1)/2 is the nth triangular number and the indexing with ...

A noncayley graph is a graph which is not a Cayley graph. All graphs that are not vertex-transitive are noncayley graphs. However, some vertex-transitive graph are noncayley. ...

The concept of "random close packing" was shown by Torquato et al. (2000) to be mathematically ill-defined idea that is better replaced by the notion of "maximally random ...

The triangle DeltaA^*B^*C^* obtained by reflecting the vertices of a reference triangle DeltaABC about the opposite sides is called the reflection triangle (Grinberg 2003). ...