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...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: ...

...ers topics including whole numbers, the extraction of roots and irrational numbers.<ref>{{citation|doi=10.1007/978-0-85729-862-1_10|title=Robert Recorde: Tudo ...factorization ''sursolids'', distinguishing between them by use of ordinal numbers: that is, he defined 5 as the ''first sursolid'', written as '''ʃz''' and 7 ...

[[Image:Herman Standard.png|200px|right|thumb|The Julia set of the cubic rational function ''e''^2&pi;''it''''z''²(''z''&minus; ...06.</ref> where the [[rational function]] is conformally conjugate to an [[irrational rotation]] of the standard [[annulus (mathematics)|annulus]]. ...

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

...C. Williams: Computation of the class number and class group of a complex cubic field. Math. Comp. 45 (1985), no. 171, 223&ndash;231. {{MR|790655}}</ref> a ...te Scheidler|R. Scheidler]]: Ideal arithmetic and infrastructure in purely cubic function fields. (English, French summary) J. Théor. Nombres Bordeaux 13 (2 ...

| rationality=irrational algebraic ...s that the supersilver ratio is found as the unique real solution of the [[cubic equation]] ...

...] triangle which is [[obtuse triangle|obtuse]] with an [[irrational number|irrational]] but [[algebraic number|algebraic]] ratio between the lengths of its sides ...ay |last2=Guy |first2=R.K. |author-link2=Richard K. Guy |title=The Book of Numbers |year=1996 |publisher=Springer-Verlag |location=New York|page=206|contribut ...

| rationality=irrational algebraic ...s that the supergolden ratio is found as the unique real solution of the [[cubic equation]] <math>\psi^{3} - \psi^{2} - 1 = 0.</math> The decimal expansion ...

...ion|compass and straight edge]], and the values are called [[constructible numbers]]. ...], whereas if the codomain is taken to be the [[projectively extended real numbers]], these entries take the value <math>\infty</math> (see [[division by zero ...

...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 ...

...nal [[geometry]] and vibrating lyre strings; his group also discover the [[irrational number|irrationality]] of the [[square root]] of [[two]], ...erations, [[geometry]], operations with [[fractions]], simple equations, [[cubic equations]], quartic equations, and [[permutations]] and [[combinations]] ...

...t extends the [[Fibonacci sequence]] to the index set of positive rational numbers, <math> \mathbf{Q}^+ </math>. Many known Fibonacci identities carry over t ...rank-2 pseudolattices and is related to the arithmetic of real [[Quadratic irrational number|quadratic irrationals]]. ...

...raic integer]]s of degree two. Thus quadratic integers are those complex numbers that are solutions of equations of the form ...aussian integer]]s. Another common example is the non-[[real number|real]] cubic [[root of unity]] <math display=inline>\frac{-1+\sqrt{-3}}{2}</math>, which ...

...nomial]]s may determine whether or not the spectrum is empty for algebraic numbers ''a'' of all degrees.<ref>{{harvnb|Stein|2004|p=21}}; {{harvnb|Jepsen|Monsk ...idissection was impossible if the coordinates of the vertices are rational numbers with odd denominators. He submitted this proof to ''[[Mathematics Magazine] ...

...between rational and irrational numbers, and simply calculated irrational numbers to the required degree of precision.<ref>Shen, pp.27, 36–37</ref> ..., who explicitly acknowledged his source: "My method of finding square and cubic roots was based on the Jia Xian method in ''Shi Suo Suan Shu''."<ref>Wu Wen ...

...al [[geometry]] and vibrating lyre strings; his group also discovers the [[irrational number|irrationality]] of the [[square root of two]]. ...India, write the ''Surya Prajinapti'', a mathematical text classifying all numbers into three sets: enumerable, innumerable and [[Infinite set|infinite]]. It ...

...ert|Johann Lambert]] found that pi cannot be a ratio and is therefore an [[irrational number]]. Pi shows up in many areas having no obvious connection to circles ...ynomial]]s can approximate sines and cosines. Includes information about [[cubic spline]]s in design engineering.<ref name="Polynomials" /> ...

...ies like this one are useful for looking up, comparing and reviewing large numbers of terms together. You can help enhance this page by adding new terms or wr {{defn|defn=An [[series (mathematics)|infinite series]] of numbers is said to '''converge absolutely''' (or to be '''absolutely convergent''') ...

...logram, was based on the mass of a [[volume]] of water of one [[litre]] (a cubic [[decimetre]]). Reference copies for both units were manufactured in platin ...arly [[medieval era]], [[Roman numerals]] were used in Europe to represent numbers,<ref> ...

...>\infty</math>,}} the ''critical line'' of nontrivial zeros with [[Complex numbers#Definition and basic operations|Re(''z'')]] = 1/2 and slopes of absolute va ...mber theory]] because it implies results about the distribution of [[prime numbers]]. It was proposed by {{harvs|txt|first=Bernhard|last= Riemann|year=1859|au ...