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- Milü abstract "The name Milü (Chinese: 密率; pinyin: mì lǜ; "detailed (approximation) ratio"), also known as Zulü (Zu's ratio), is given to an approximation to π (pi) found by Chinese mathematician and astronomer Zǔ Chōngzhī (祖沖之). He computed π to be between 3.1415926 and 3.1415927 and gave two rational approximations of π, 22/7 and 355/113, naming them respectively Yuelü 约率 (approximate ratio) and Milü.355/113 is the best rational approximation of π with a denominator of four digits or fewer, being accurate to 6 decimal places. It is within 0.000009% of the value of π, or in terms of common fractions overestimates π by less than 1/3 748 629. The next rational number (ordered by size of denominator) that is a better rational approximation of π is 52 163/16 604, still only correct to 6 decimal places and hardly closer to π than 355/113. To be accurate to 7 decimal places, one needs to go as far as 86 953/27 678. For 8, we need 102 928/32 763. 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 π ≈ 355/113 can be obtained with He Chengtian's method".
- Milü thumbnail Diaorifa.GIF?width=300.
- Milü wikiPageID "7315901".
- Milü wikiPageRevisionID "600678422".
- Milü c "密率".
- Milü p "mì lǜ".
- Milü subject Category:Pi.
- Milü comment "The name Milü (Chinese: 密率; pinyin: mì lǜ; "detailed (approximation) ratio"), also known as Zulü (Zu's ratio), is given to an approximation to π (pi) found by Chinese mathematician and astronomer Zǔ Chōngzhī (祖沖之).".
- Milü label "Milü".
- Milü label "Milü".
- Milü label "密率".
- Milü sameAs Mil%C3%BC.
- Milü sameAs Milü.
- Milü sameAs Q3858176.
- Milü sameAs Q3858176.
- Milü wasDerivedFrom Milü?oldid=600678422.
- Milü depiction Diaorifa.GIF.
