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...n to irrational numbers that are not quadratic by using either [[quadratic irrational]]s or simply [[rational number]]s. It is named after [[Harold Davenport]] Given a number α which is either rational or a quadratic irrational, we can find unique integers ''x'', ''y'', and ''z'' such that ''x'', ''y'' ...

...'''Kleinian ring''', which is the [[ring of integers]] in the imaginary [[quadratic field]] <math>\mathbb{Q}(\sqrt{-7})</math>. This ring is a [[unique factori <!--[[Category:Algebraic numbers]]-->[[Category:Quadratic irrational numbers]] ...

...periodic precisely when the original number is a cubic [[Irrational number|irrational]]. A standard way of writing real numbers is by their [[decimal representation]], such as: ...

{{short description|Special type of irrational number}} ...''' (sometimes spelled '''Bruno''' or '''Bryuno''') is a special type of [[irrational number]] named for Russian mathematician [[Alexander Bruno]], who introduce ...

...ov spectrum''', devised by [[Andrey Markov]], is a complicated set of real numbers arising in [[Markov number|Markov Diophantine equations]] and also in the t == Quadratic form characterization == ...

{{short description|Property of an irrational number}} ...r solutions to the Markov Diophantine equation|Markov number|a set of real numbers|Markov spectrum}} ...

...06.</ref> where the [[rational function]] is conformally conjugate to an [[irrational rotation]] of the standard [[annulus (mathematics)|annulus]]. and an [[irrational number]] <math>\theta</math>, such that ...

{{Short description|Concept in the geometry of numbers}} In the [[geometry of numbers]], the '''Klein polyhedron''', named after [[Felix Klein]], is used to gene ...

...ral numbers. Natural numbers including 0 are also sometimes called ''whole numbers''.<ref> ...ath>\mathbb{Z}</math>): Positive and [[negative number|negative]] counting numbers, as well as zero: {..., −3, −2, −1, 0, 1, 2, 3, ...}. ...

{{short description|Root of a quadratic polynomial with a unit leading coefficient}} ...raic integer]]s of degree two. Thus quadratic integers are those complex numbers that are solutions of equations of the form ...

{{short description|Book on the geometry of numbers}} '''''The Geometry of Numbers''''' is a book on the [[geometry of numbers]], an area of mathematics in which the geometry of [[Lattice (group)|lattic ...

...lso described by R. Schoof<ref name="schoof-infrastructure1">R. J. Schoof: Quadratic fields and factorization. Computational methods in number theory, Part II, ...s group.<ref name="paulus-rueck">S. Paulus, H.-G. Rück: Real and imaginary quadratic representations of hyperelliptic function fields. (English summary) Math. C ...

...t extends the [[Fibonacci sequence]] to the index set of positive rational numbers, <math> \mathbf{Q}^+ </math>. Many known Fibonacci identities carry over t ...ces and is related to the arithmetic of real [[Quadratic irrational number|quadratic irrationals]]. ...

...\beta_1,...,\beta_n\}</math> is [[linearly independent]] over the rational numbers, then the number <math>\alpha_1^{\beta_1}\alpha_2^{\beta_2}\cdots\alpha_n^{ ...=Goldfeld | first=Dorian | title=Gauss' class number problem for imaginary quadratic fields | journal=Bulletin of the American Mathematical Society | publisher= ...

|rationality=Irrational ...the included two cubes) equal to the square roots of the first six natural numbers, up to the square root of 6.]] --> ...

|rationality=Irrational It is an [[irrational number|irrational]] [[algebraic number]]. The first sixty significant digits of its [[decima ...

...re ''a'' is [[algebraic number|algebraic]] and ''b'' is a real [[quadratic irrational]], are [[transcendental number|transcendental]]. In particular, this result ...

...right|thumb|240px|The number [[Square root of 2|<math>\sqrt{2}</math>]] is irrational.]] ...two [[integer]]s. When the [[ratio]] of lengths of two line segments is an irrational number, the line segments are also described as being ''[[commensurability ...

...nding all imaginary [[quadratic field]]s with [[Class numbers of imaginary quadratic fields|class number]] 1. ...f [[complex number]]s and <math>\overline{\Q}</math> denotes the algebraic numbers (the algebraic closure of the [[rational number]]s <math>\Q</math>). Using ...

{{short description|Subset of real numbers that are greater than zero}} ...hose [[real number]]s that are greater than zero. The '''non-negative real numbers''', <math>\R_{\geq 0} = \left\{ x \in \R \mid x \geq 0 \right\},</math> als ...