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The quotient W(p)=((p-1)!+1)/p which must be congruent to 0 (mod p) for p to be a Wilson prime. The quotient is an integer only when p=1 (in which case W(1)=2) or p is a ...

The n-hypersphere (often simply called the n-sphere) is a generalization of the circle (called by geometers the 2-sphere) and usual sphere (called by geometers the 3-sphere) ...

A riffle shuffle, also called the Faro shuffle, is a shuffle in which a deck of 2n cards is divided into two halves. The top half of the deck is placed in the left hand, and ...

The set of graph eigenvalues of the adjacency matrix is called the spectrum of the graph. (But note that in physics, the eigenvalues of the Laplacian matrix of a graph are ...

A contravariant tensor is a tensor having specific transformation properties (cf., a covariant tensor). To examine the transformation properties of a contravariant tensor, ...

If two perpendicular lines are drawn through the orthocenter H of any triangle, these lines intercept each side (or its extension) in two points (labeled P_(12), P_(12)^', ...

An embedding is a representation of a topological object, manifold, graph, field, etc. in a certain space in such a way that its connectivity or algebraic properties are ...

An operation on rings and modules. Given a commutative unit ring R, and a subset S of R, closed under multiplication, such that 1 in S, and 0 not in S, the localization of R ...

Let K be a field of arbitrary characteristic. Let v:K->R union {infty} be defined by the following properties: 1. v(x)=infty<=>x=0, 2. v(xy)=v(x)+v(y) forall x,y in K, and 3. ...

A set of four points, one of which is the orthocenter of the other three. In an orthocentric system, each point is the orthocenter of the triangle of the other three, as ...