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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 Euclid's orchard ： ウィキペディア英語版 Euclid's orchard In mathematics, informally speaking, Euclid's orchard is an array of one-dimensional "trees" of unit height planted at the lattice points in one quadrant of a square lattice. More formally, Euclid's orchard is the set of line segments from (''i'', ''j'', 0) to (''i'', ''j'', 1) where ''i'' and ''j'' are positive integers. The trees visible from the origin are those at lattice points (''m'', ''n'', 0) where ''m'' and ''n'' are coprime, i.e., where the fraction m⁄n is in reduced form. The name ''Euclid's orchard'' is derived from the Euclidean algorithm. If the orchard is projected relative to the origin onto the plane ''x''+''y''=1 (or, equivalently, drawn in perspective from a viewpoint at the origin) the tops of the trees form a graph of Thomae's function. The point (''m'', ''n'', 1) projects to : $\backslash left\; (\; \backslash frac\; ,\; \backslash frac\; ,\; \backslash frac\; \backslash right\; ).$ ==See also== *Opaque forest problem 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「Euclid's orchard」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.