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A quantity which takes on the value zero is said to vanish. For example, the function f(z)=z^2 vanishes at the point z=0. For emphasis, the term "vanish identically" is ...

Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

The Dedekind eta function is defined over the upper half-plane H={tau:I[tau]>0} by eta(tau) = q^_^(1/24)(q^_)_infty (1) = q^_^(1/24)product_(k=1)^(infty)(1-q^_^k) (2) = ...

The toroidal crossing number cr_(1)(G) of a graph G is the minimum number of crossings with which G can be drawn on a torus. A planar graph has toroidal crossing number 0, ...

The term "arbelos" means shoemaker's knife in Greek, and this term is applied to the shaded area in the above figure which resembles the blade of a knife used by ancient ...

A topological space X such that for every closed subset C of X and every point x in X\C, there is a continuous function f:X->[0,1] such that f(x)=0 and f(C)={1}. This is the ...

The expression im kleinen is German and means "on a small scale." A topological space is connected im kleinen at a point x if every neighborhood U of x contains an open ...

The directional derivative del _(u)f(x_0,y_0,z_0) is the rate at which the function f(x,y,z) changes at a point (x_0,y_0,z_0) in the direction u. It is a vector form of the ...

The Lebesgue covering dimension is an important dimension and one of the first dimensions investigated. It is defined in terms of covering sets, and is therefore also called ...

A topological space X is locally compact if every point has a neighborhood which is itself contained in a compact set. Many familiar topological spaces are locally compact, ...