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The name Milü (; "detailed (approximation) ratio"), also known as Zulü (Zu's ratio), is given to an approximation to (pi) found by Chinese mathematician and astronomer Zǔ Chōngzhī (祖沖之). He computed to be between 3.1415926 and 3.1415927 and gave two rational approximations of , and , naming them respectively Yuelü 约率 (approximate ratio) and Milü. is the best rational approximation of with a denominator of four digits or fewer, being accurate to 6 decimal places. It is within 0.000009% of the value of , or in terms of common fractions overestimates by less than . The next rational number (ordered by size of denominator) that is a better rational approximation of is , still only correct to 6 decimal places and hardly closer to than . To be accurate to 7 decimal places, one needs to go as far as . For 8, we need . : An easy mnemonic helps memorize this useful fraction by writing down each of the first three odd numbers twice: 1 1 3 3 5 5, then dividing the decimal number represented by the last 3 digits by the decimal number given by the first three digits. Zu's contemporary calendarist and mathematician He Chengtian (何承天) invented a fraction interpolation method called "harmonization of the divisor of the day" to obtain a closer approximation by iteratively adding the numerators and denominators of a "weak" fraction and a "strong" fraction. Zu Chongzhi's approximation ≈ can be obtained with He Chengtian's method〔Wu Wenjun ed Grand Series of History of Chinese Mathematics vol 4 p125〕 == See also == *Continued fraction expansions of *History of numerical approximations of *Pi Approximation Day 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「Milü」の詳細全文を読む スポンサード リンク
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