The Chinese put a lot of emphasis on computing 
, the ratio a circle's circumference to its diameter. The computation of was an area of mathematics where the Chinese were far ahead of the Western world. From the Arithmetic in Nine Sections, the area of a circle is approximated as 3/4 
the square of the diameter, or one-twelfth of the square of the circumference, which is consistent with a value of 3 for .
Much progress was made in computing during the Post-Han period, which lasted from 220AD to around 600AD. In the third Century, a general named Wang Fu established the rational approximation 144/45 for , which gives a value of around 3.1511. Slightly after Wang Fu, Liu Hui established the relation 3.1410 < < 3.1427.
During the 5th Century, Tsu Ch’ung-chi and his son did even better, finding that
< 3.1415927and arriving at the rational approximation = 355/113, which yields correct to 6 decimal places. This level of precision was not surpassed until 1420, when was found correct to 16 places by Jamshid Al-Kashr of Smirkand. Western mathematics did not surpass the approximation of Tsu until around 1600. Tsu’s achievements were considered so remarkable that a landmark on the moon now bears his name.
The approximation of
Tsu Ch’ung Chi
