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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 Minkowski's question mark function ： ウィキペディア英語版 Minkowski's question mark function In mathematics, the Minkowski question mark function (or the slippery devil's staircase), denoted by , is a function possessing various unusual fractal properties, defined by . It maps quadratic irrationals to rational numbers on the unit interval, via an expression relating the continued fraction expansions of the quadratics to the binary expansions of the rationals, given by Arnaud Denjoy in 1938. In addition, it maps rational numbers to dyadic rationals, as can be seen by a recursive definition closely related to the Stern–Brocot tree. ==Definition== If $(a\_1,\; a\_2,\; \backslash ldots)$ is the continued fraction representation of an irrational number , then :$(x)\; =\; a\_0\; +\; 2\; \backslash sum\_^\backslash infty\; \backslash frac\}$ whereas: If $(a\_1,\; a\_2,\; \backslash ldots,\; a\_m)$ is a continued fraction representation of a rational number , then :$(x)\; =\; a\_0\; +\; 2\; \backslash sum\_^m\; \backslash frac\}$ 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「Minkowski's question mark function」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.