Zu Chongzhi calculates c. 480 AD that 3.1415926 < π < 3.1415927, with 7 correct decimals, and the rational approximation 355/113 (milü), the most precise fraction possible with a denominator under 16,600. Applied to Earth's circumference, it produces an error under 0.6 mm. He uses Liu Hui's polygon algorithm applied to a 24,576-sided polygon. This precision record was not surpassed until Al-Kashi calculated 16 decimals in 1424. The main work, the Zhui Shu, was lost during the Song dynasty; the result is known only through secondary sources (Song Shu, Sui Shu). Zu Chongzhi also developed the Daming calendar (465 AD), with a year of 365.24281 days (an error of 50 seconds relative to the modern value).