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An automorphism which interchanges the two vertices of a regular map at each edge without interchanging the vertices.

In a local ring R, there is only one maximal ideal m. Hence, R has only one quotient ring R/m which is a field. This field is called the residue field.

The Rutherford constant is a mathematical constant that arises in plasma physics and is defined by K_R = sqrt(2)int_(-1)^infty([R(x)]^2)/(S[x])dx (1) = 0.8227..., (2) where ...

Let A=a_(ij) be an n×n matrix with complex (or real) entries and eigenvalues lambda_1, lambda_2, ..., lambda_n, then sum_(i=1)^n|lambda_i|^2<=sum_(i,j=1)^n|a_(ij)|^2 (1) ...

The bias of a series is defined as Q[a_i,a_(i+1),a_(i+2)]=(a_ia_(i+2)-a_(i+1)^2)/(a_ia_(i+1)a_(i+2)). A series is geometric iff Q=0. A series is artistic iff the bias is ...

An affine transformation that preserves area.

A star polygon-like figure {p/q} for which p and q are not relatively prime. Examples include the hexagram {6/2}, star of Lakshmi {8/2}, and nonagram {9/3}.

Two points z and z^S in C^* are symmetric with respect to a circle or straight line L if all circles and straight lines passing through z and z^S are orthogonal to L. Möbius ...

Given any two distinct points x,y, there exist neighborhoods u and v of x and y, respectively, with u intersection v=emptyset. It then follows that finite subsets are closed.

The third Brocard triangle is Gibert's term for the isogonal conjugate of the first Brocard triangle. It has trilinear vertex matrix [b^2c^2 ab^3 ac^3; a^3b a^2c^2 bc^3; a^3c ...