Minggatu

Also known as Zi Jingan

Minggatu, courtesy name Jing'an, was a Mongol of the Plain White Banner who entered the Directorate of Astronomy as a banner student under Kangxi and served there for more than fifty years. He worked on the later supplement to the Thorough Investigation of Calendrical Astronomy, completed in 1742, and on the treatise on astronomical instruments, and in 1756 and 1759 joined survey parties in Xinjiang that fixed latitudes and longitudes for the Qianlong imperial atlas; in 1759 he became director of the Directorate. The French Jesuit Pierre Jartoux had brought three trigonometric series to China without proofs, and Minggatu spent some thirty years deriving them and adding six formulas of his own. His son Mingxin and student Chen Jixin completed his four-chapter Quick Methods for Accurate Circle Division (Geyuan milu jiefa) in 1774, and a sequence of numbers arising in its derivations matches what Western mathematics later named the Catalan numbers.