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The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...

A Poisson process is a process satisfying the following properties: 1. The numbers of changes in nonoverlapping intervals are independent for all intervals. 2. The ...

A foliation F of dimension p on a manifold M is transversely orientable if it is integral to a p-plane distribution D on M whose normal bundle Q is orientable. A p-plane ...

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, ...

Let A be an edge cut of a connected graph G. Then the cyclic edge connectivity lambda_c(G) is the size of a smallest cyclic edge cut, i.e., a smallest edge cut A such that ...

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 ...

A graph embedding, sometimes also called a graph drawing, is a particular drawing of a graph. Graph embeddings are most commonly drawn in the plane, but may also be ...

The constant pi, denoted pi, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r, pi = C/d (1) = C/(2r) (2) pi has decimal expansion ...