[CoreDumpling]

In Chinese the fraction 355/113 has been known as the 密率 ("detailed ratio") and 22/7 as the 约率 ("approximate ratio"). It is documented in the Book of Sui, volume 16:

宋末，南徐州從事史祖沖之，更開密法，以圓徑一億為一丈，圓周盈數三丈一尺四寸一分五厘九毫二秒七忽，朒數三丈一尺四寸一分五厘九毫二秒六忽，正數在盈朒二限之間。密率，圓徑一百一十三，圓周三百五十五。約率，圓徑七，週二十二。 [1]

While it suggests that the value was calculated around the end of the Liu Song Dynasty (~479 CE) by Zu Chongzhi to have an upper bound of 3.1415927 and lower bound of 3.1415926, the 密法 method is not explained.

It has been thought that Zu may have used a "method of averaging days" to calculate an intermediate value between two prior known approximations of 22/7 and 157/50 [2]. Not a very satisfying result for anyone who wants to find something special in the numbers 355 and 113.

[1] https://zh.wikisource.org/wiki/%E9%9A%8B%E6%9B%B8/%E5%8D%B71...

[2] http://books.google.com/books?id=QlbzjN_5pDoC&lpg=PA34&#...