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In mathematics, the Farey sequence of order ''n'' is the sequence of completely reduced fractions between 0 and 1 which, when in lowest terms, have denominators less than or equal to ''n'', arranged in order of increasing size. Each Farey sequence starts with the value 0, denoted by the fraction 0⁄1, and ends with the value 1, denoted by the fraction 1⁄1 (although some authors omit these terms). A Farey sequence is sometimes called a Farey series, which is not strictly correct, because the terms are not summed. ==Examples== The Farey sequences of orders 1 to 8 are : :''F''1 = :''F''2 = :''F''3 = :''F''4 = :''F''5 = :''F''6 = :''F''7 = :''F''8 = |- |''F''3 = |- |''F''4 = |- |''F''5 = |- |''F''6 = |- |''F''7 = |- |''F''8 = |} F3 = F4 = F5 = F6 = F7 = F8 = |} 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「Farey sequence」の詳細全文を読む スポンサード リンク
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