翻訳と辞書 Words near each other ・ Gausfred II of Roussillon ・ Gausfred III of Roussillon ・ Gausganj ・ Gaushala Bazar ・ Gaushala, Nepal ・ Gaushorn ・ Gausian dynasty ・ Gauslaa ・ Gauss (crater) ・ Gauss (disambiguation) ・ Gauss (ship) ・ GAUSS (software) ・ Gauss (surname) ・ Gauss (unit) ・ Gauss Centre for Supercomputing ・ Gauss circle problem ・ Gauss expedition ・ Gauss Glacier ・ Gauss iterated map ・ Gauss Lectureship ・ Gauss lens ・ Gauss map ・ Gauss map (disambiguation) ・ Gauss Moutinho Cordeiro ・ Gauss Peninsula ・ Gauss pseudospectral method ・ Gauss Research Laboratory ・ Gauss Speaker Company ・ GAUSS Srl ・ Gauss sum Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Gauss circle problem ： ウィキペディア英語版 Gauss circle problem In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centred at the origin and with radius ''r''. The first progress on a solution was made by Carl Friedrich Gauss, hence its name. ==The problem== Consider a circle in R2 with centre at the origin and radius ''r'' ≥ 0. Gauss' circle problem asks how many points there are inside this circle of the form (''m'',''n'') where ''m'' and ''n'' are both integers. Since the equation of this circle is given in Cartesian coordinates by ''x''2 + ''y''2 = ''r''2, the question is equivalently asking how many pairs of integers ''m'' and ''n'' there are such that :$m^2+n^2\backslash leq\; r^2.$ If the answer for a given ''r'' is denoted by ''N''(''r'') then the following list shows the first few values of ''N''(''r'') for ''r'' an integer between 0 and 12 followed by the list of values $\backslash pi\; r^2$ rounded to the nearest integer: :1, 5, 13, 29, 49, 81, 113, 149, 197, 253, 317, 377, 441 :0, 3, 13, 28, 50, 79, 113, 154, 201, 254, 314, 380, 452 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「Gauss circle problem」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.