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An graph edge of a graph is separating if a path from a point A to a point B must pass over it. Separating graph edges can therefore be viewed as either bridges or dead ends.

The triangular cupola is Johnson solid J_3. Its faces consist of 4 equilateral triangles, 3 squares, and 1 hexagon. It is implemented in the Wolfram Language as ...

The trivial loop is the loop that takes every point to its basepoint. Formally, if X is a topological space and x in X, the trivial loop based at x is the map L:[0,1]->X ...

The vercosine, written vercos(z) and also known as the "versed cosine," is a little-used trigonometric function defined by vercos(z) = 2cos^2(1/2z) (1) = 1+cosz, (2) where ...

A map which is monotone increasing and therefore order-preserving.

The notation R^_ denotes the set of affinely extended real numbers.

The point of illumination for a caustic.

The vector r from the origin to the current position. It is also called the position vector. The derivative of r satisfies ...

If F is an algebraic Galois extension field of K such that the Galois group of the extension is Abelian, then F is said to be an Abelian extension of K. For example, ...

In the American system, one billion equals 10^9=1000000000. In the French and German systems, one billion equals 10^(12). In recent years, the "American" system has become ...