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Prince Rupert's cube is the largest cube that can be made to pass through a given cube. In other words, the cube having a side length equal to the side length of the largest ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

The sample mean of a set {x_1,...,x_n} of n observations from a given distribution is defined by m=1/nsum_(k=1)^nx_k. It is an unbiased estimator for the population mean mu. ...

A separable extension K of a field F is one in which every element's algebraic number minimal polynomial does not have multiple roots. In other words, the minimal polynomial ...

For a graph G and a subset S^t of the vertex set V(G), denote by N_G^t[S^t] the set of vertices in G which are adjacent to a vertex in S^t. If N_G^t[S^t]=V(G), then S^t is ...

A tube of radius r of a set gamma is the set of points at a distance r from gamma. In particular, if gamma(t) is a regular space curve whose curvature does not vanish, then ...

Linear Algebra

A bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent. A ...

An order-n Costas array is a permutation on {1,...,n} such that the distances in each row of the triangular difference table are distinct. For example, the permutation ...

Hex is a two-player game invented by Piet Hein in 1942 while a student at Niels Bohr's Institute for Theoretical Physics, and subsequently and independently by John Nash in ...