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Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...

If A moves along a known curve, then P describes a pursuit curve if P is always directed toward A and A and P move with uniform velocities. Pursuit curves were considered in ...

The Skewes number (or first Skewes number) is the number Sk_1 above which pi(n)<li(n) must fail (assuming that the Riemann hypothesis is true), where pi(n) is the prime ...

How can n points be distributed on a unit sphere such that they maximize the minimum distance between any pair of points? This maximum distance is called the covering radius, ...

The stella octangula is a polyhedron compound composed of a tetrahedron and its dual (a second tetrahedron rotated 180 degrees with respect to the first). The stella ...

Consider the average length of a line segment determined by two points picked at random in the interior of an arbitrary triangle Delta(a,b,c) with side lengths a, b, and c. ...

The truncated great dodecahedral graph is the skeleton of the small stellated truncated dodecahedron and truncated great dodecahedron. It is illustrated above in a number of ...

A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...

Hilbert's problems are a set of (originally) unsolved problems in mathematics proposed by Hilbert. Of the 23 total appearing in the printed address, ten were actually ...