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The cycloid is the locus of a point on the rim of a circle of radius a rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find ...

The Delannoy numbers D(a,b) are the number of lattice paths from (0,0) to (b,a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed (i.e., ->, ^, ...

The Errera graph is the 17-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

The great icosahedron, not to be confused with the great icosidodecahedron orgreat icosicosidodecahedron, is the Kepler-Poinsot polyhedronhose dual is the great stellated ...

The great stellated dodecahedron is one of the Kepler-Poinsot polyhedra. It is also the uniform polyhedron with Maeder index 52 (Maeder 1997), Wenninger index 22 (Wenninger ...

An out-shuffle, also known as a perfect shuffle (Golomb 1961), is a riffle shuffle in which the top half of the deck is placed in the right hand, and cards are then ...

A perfect graph is a graph G such that for every induced subgraph of G, the clique number equals the chromatic number, i.e., omega(G)=chi(G). A graph that is not a perfect ...

An analog of the polyominoes and polyiamonds in which collections of regular hexagons are arranged with adjacent sides. They are also called hexes, hexas, or polyfrobs ...

A root of a polynomial P(z) is a number z_i such that P(z_i)=0. The fundamental theorem of algebra states that a polynomial P(z) of degree n has n roots, some of which may be ...

The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...