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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kronecker's theorem ： ウィキペディア英語版 Kronecker's theorem In mathematics, Kronecker's theorem is a theorem about diophantine approximation, introduced by . Kronecker's approximation theorem had been firstly proved by L. Kronecker in the end of the 19th century. It has been now revealed to relate to the idea of n-torus and Mahler measure since the later half of the 20th century. In terms of physical systems, it has the consequence that planets in circular orbits moving uniformly around a star will, over time, assume all alignments, unless there is an exact dependency between their orbital periods. == Statement == Kronecker's theorem is a result in diophantine approximations applying to several real numbers ''xi'', for 1 ≤ ''i'' ≤ ''n'', that generalises Dirichlet's approximation theorem to multiple variables. The classical Kronecker's approximation theorem is formulated as follows; Given real numbers $\backslash alpha\_i=(\backslash alpha\_,\backslash cdots,\backslash alpha\_)\backslash in\backslash mathbb^n,\; i=1,\backslash cdots,m$ and $\backslash beta\_j=(\backslash beta\_1,\backslash cdots,\backslash beta\_n)\backslash in\; \backslash mathbb^n$ , for any small $\backslash epsilon>0$ there exist integers $p\_i$ and $q\_j$ such that : , if and only if for any $r\_1,\backslash dots,r\_n\backslash in\backslash mathbb,\backslash \; i=1,\backslash dots,m$ with :$\backslash sum^n\_\backslash alpha\_r\_j\backslash in\backslash mathbb,\; \backslash \; \backslash \; i=1,\backslash dots,m\backslash \; ,$ the number $\backslash sum^n\_\backslash beta\_jr\_j$ is also an integer. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kronecker's theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.