Milú

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.

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