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A transformation in which coordinates in two spaces are expressed rationally in terms of those in another.

The Riemann sphere C^*=C union {infty}, also called the extended complex plane. The notation C^^ is sometimes also used (Krantz 1999, p. 82). The notation C^* is also used to ...

The mathematical study of how to manipulate the parameters affecting the behavior of a system to produce the desired or optimal outcome.

A reciprocity theorem for the case n=3 solved by Gauss using "integers" of the form a+brho, when rho is a root of x^2+x+1=0 (i.e., rho equals -(-1)^(1/3) or (-1)^(2/3)) and ...

A schematic mathematical illustration showing the relationships between or properties of mathematical objects.

The invariance of domain theorem states that if f:M->N is a one-to-one and continuous map between n-manifolds without boundary, then f is an open map.

The Dürer graph is the skeleton of Dürer's solid, which is the generalized Petersen graph GP(6,2). It is illustrated above in a number of embeddings. It is implemented in the ...

Edge splitting is the reverse of edge contraction.

Given positive numbers s_a, s_b, and s_c, the Elkies point is the unique point Y in the interior of a triangle DeltaABC such that the respective inradii r_a, r_b, r_c of the ...

An event is a certain subset of a probability space. Events are therefore collections of outcomes on which probabilities have been assigned. Events are sometimes assumed to ...