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Let p_n/q_n be the sequence of convergents of the continued fraction of a number alpha. Then a Brjuno number is an irrational number such that ...

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 ...

A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

A set A in a first-countable space is dense in B if B=A union L, where L is the set of limit points of A. For example, the rational numbers are dense in the reals. In ...

A number is said to be simply normal to base b if its base-b expansion has each digit appearing with average frequency tending to b^(-1). A normal number is an irrational ...

The number 13.

Somos defines a rational triangle as a triangle such that all three sides measured relative to each other are rational. Koblitz (1993) defined a congruent number as an ...

Given an expression involving known constants, integration in finite terms, computation of limits, etc., the constant problem is the determination of if the expression is ...

A friend of a number n is another number m such that (m,n) is a friendly pair.

Two lengths are called incommensurate or incommensurable if their ratio cannot be expressed as a ratio of whole numbers. Irrational numbers and transcendental numbers are ...