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The spectrum of a ring is the set of proper prime ideals, Spec(R)={p:p is a prime ideal in R}. (1) The classical example is the spectrum of polynomial rings. For instance, ...

Specifying two adjacent angles A and B and the side between them c uniquely (up to geometric congruence) determines a triangle with area K=(c^2)/(2(cotA+cotB)). (1) The angle ...

A theorem from information theory that is a simple consequence of the weak law of large numbers. It states that if a set of values X_1, X_2, ..., X_n is drawn independently ...

The "natural exponential function" is the name sometimes given in elementary contexts to the function f(x)=e^x, where e =2.718... is the base of the natural logarithm. While ...

The algorithm for the construction of a Gröbner basis from an arbitrary ideal basis. Buchberger's algorithm relies on the concepts of S-polynomial and polynomial reduction ...

In the hyperbolic plane H^2, a pair of lines can be parallel (diverging from one another in one direction and intersecting at an ideal point at infinity in the other), can ...

Given a field F and an extension field K superset= F, if alpha in K is an algebraic element over F, the minimal polynomial of alpha over F is the unique monic irreducible ...

Let K be a number field and let O be an order in K. Then the set of equivalence classes of invertible fractional ideals of O forms a multiplicative Abelian group called the ...

A famous perceptual illusion in which the brain switches between seeing a young girl and an old woman (or "wife" and "mother in law"). An anonymous German postcard from 1888 ...

Guy's "strong law of small numbers" states that there aren't enough small numbers to meet the many demands made of them. Guy (1988) also gives several interesting and ...