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Hurwitz's theorem (number theory) : ウィキペディア英語版
Hurwitz's theorem (number theory)

In number theory, Hurwitz's theorem, named after Adolf Hurwitz, gives a bound on a Diophantine approximation. The theorem states that for every irrational number ''ξ'' there are infinitely many relatively prime integers ''m'', ''n'' such that
:\left |\xi-\frac\right |<\frac.
The hypothesis that ''ξ'' is irrational cannot be omitted. Moreover the constant \scriptstyle \sqrt is the best possible; if we replace \scriptstyle \sqrt by any number \scriptstyle A > \sqrt and we let \scriptstyle \xi=(1+\sqrt)/2 (the golden ratio) then there exist only ''finitely'' many relatively prime integers ''m'', ''n'' such that the formula above holds.
== References ==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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