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A hyperbolic knot is a knot that has a complement that can be given a metric of constant curvature -1. All hyperbolic knots are prime knots (Hoste et al. 1998). A prime knot ...

A game played on a board of a given shape consisting of a number of holes of which all but one are initially filled with pegs. The goal is to remove all pegs but one by ...

A plane partition is a two-dimensional array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n. In ...

The word "rigid" has two different meaning when applied to a graph. Firstly, a rigid graph may refer to a graph having a graph automorphism group containing a single element. ...

A superellipse is a curve with Cartesian equation |x/a|^r+|y/b|^r=1, (1) first discussed in 1818 by Lamé. A superellipse may be described parametrically by x = acos^(2/r)t ...

A tiling of regular polygons (in two dimensions), polyhedra (three dimensions), or polytopes (n dimensions) is called a tessellation. Tessellations can be specified using a ...

A uniquely k-colorable graph G is a chi-colorable graph such that every chi-coloring gives the same partition of G (Chao 2001). Examples of uniquely minimal colorable classes ...

The third prime number, which is also the second Fermat prime, the third Sophie Germain prime, and Fibonacci number F_4. It is an Eisenstein prime, but not a Gaussian prime, ...

The smallest composite squarefree number (2·3), and the third triangular number (3(3+1)/2). It is the also smallest perfect number, since 6=1+2+3. The number 6 arises in ...

The Archimedean duals are the 13 duals of the 13 Archimedean solids, sometimes called the Catalan solids. They are summarized in the following table and illustrated below ...