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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 : 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 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
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