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A number of the form +/-sqrt(a), where a is a positive rational number which is not the square of another rational number is called a pure quadratic surd. A number of the ...

For algebraic alpha |alpha-p/q|<1/(q^(2+epsilon)), with epsilon>0, has finitely many solutions. Klaus Roth received a Fields medal for this result.

A symmetric function on n variables x_1, ..., x_n is a function that is unchanged by any permutation of its variables. In most contexts, the term "symmetric function" refers ...

In the fields of functional and harmonic analysis, the Littlewood-Paley decomposition is a particular way of decomposing the phase plane which takes a single function and ...

Given any real number theta and any positive integer N, there exist integers h and k with 0<k<=N such that |ktheta-h|<1/N. A slightly weaker form of the theorem states that ...

A phenomenon in which a system being forced at an irrational period undergoes rational, periodic motion which persists for a finite range of forcing values. It may occur for ...

The notation Q^_ denotes the algebraic closure of the rational numbers Q. This is equivalent to the set of algebraic numbers, sometimes denoted A.

For any real number r>=0, an irrational number alpha can be approximated by infinitely many rational fractions p/q in such a way that ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...

The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler. e is the unique number with the property ...