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If a subset S of the elements of a field F satisfies the field axioms with the same operations of F, then S is called a subfield of F. In a finite field of field order p^n, ...

In the triangle DeltaABC illustrated above, side c subtends angle ∠C. More generally, given a geometric object O in the plane and a point P, let A be the angle from one edge ...

A sultan has granted a commoner a chance to marry one of his n daughters. The commoner will be presented with the daughters one at a time and, when each daughter is ...

Trials for which the Lexis ratio L=sigma/(sigma_B), satisfies L>1, where sigma is the variance in a set of s Lexis trials and sigma_B is the variance assuming Bernoulli ...

Given a sequence of real numbers a_n, the supremum limit (also called the limit superior or upper limit), written lim sup and pronounced 'lim-soup,' is the limit of ...

An ordinary knot in three dimensions suspended in four dimensions to create a knotted 2-sphere. Suspended knots are not smooth at the poles.

The swastika curve is Cundy and Rollett's (1989, p. 71) name for the quartic plane curve with Cartesian equation y^4-x^4=xy and polar equation ...

Given a matrix A, let |A| denote its determinant. Then |A||A_(rs,pq)|=|A_(r,p)||A_(s,q)|-|A_(r,q)||A_(s,p)|, (1) where A_(u,w) is the submatrix of A formed by the ...

A symmetric design is a block design (v, k, lambda, r, b) with the same number of blocks as points, so b=v (or, equivalently, r=k). An example of a symmetric block design is ...

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 ...