page_title: Minggatu
hierarchical_section_title: Minggatu
caption_attribution_description: English: Ming Antu-Catalan number
context_page_description: Minggatu, full name Sharavyn Myangat was a Mongolian astronomer, mathematician, and topographic scientist at the Qing court. His courtesy name was Jing An.
  Minggatu was born in Plain White Banner of the Qing Empire. He was of the Sharaid clan. His name first appeared in official Chinese records in 1713, among the Kangxi Emperor's retinue, as a shengyuan of the Imperial Astronomical Bureau. He worked there at a time when Jesuit missionaries were in charge of calendar reforms. He also participated in the work of compiling and editing three very important books in astronomy and joined the team of China's area measurement.
  From 1724 up to 1759, he worked at the Imperial Observatory. He participated in drafting and editing the calendar and the study of the armillary sphere.
  His seminal work The Quick Method for Obtaining the Precise Ratio of Division of a Circle, which was completed after his death by his son Mingshin, and students, was a significant contribution to the development of mathematics in China.
  He was the first person in China who calculated infinite series and obtained more than 10 formulae.
context_section_description: Minggatu (Mongolian script: ᠮᠢᠨᠭᠭᠠᠲᠦ; Chinese: 明安图; pinyin: Ming'antu, c.1692-c. 1763), full name Sharavyn Myangat (Mongolian: Шаравын Мянгат) was a Mongolian astronomer, mathematician, and topographic scientist at the Qing court. His courtesy name was Jing An (静安).
  Minggatu was born in Plain White Banner (now Plain and Bordered White Banner, Xilin Gol League, Inner Mongolia) of the Qing Empire. He was of the Sharaid clan. His name first appeared in official Chinese records in 1713, among the Kangxi Emperor's retinue, as a shengyuan (state-subsidized student) of the Imperial Astronomical Bureau. He worked there at a time when Jesuit missionaries were in charge of calendar reforms. He also participated in the work of compiling and editing three very important books in astronomy and joined the team of China's area measurement.
  From 1724 up to 1759, he worked at the Imperial Observatory. He participated in drafting and editing the calendar and the study of the armillary sphere.
  His seminal work The Quick Method for Obtaining the Precise Ratio of Division of a Circle (Chinese: 割圜密率捷法; pinyin: Gēyuán Mìlǜ Jiéfǎ), which was completed after his death by his son Mingshin, and students (among them his most gifted pupil Chen Jihin and an intendant in the minister of finance, Zhang), was a significant contribution to the development of mathematics in China.
  He was the first person in China who calculated infinite series and obtained more than 10 formulae. In the 1730s, he first established and used what was later to be known as Catalan numbers. The Jesuit missionaries' influence can be seen by many traces of European mathematics in his works, including the use of Euclidean notions of continuous proportions, series addition, subtraction, multiplication and division, series reversion, and the binomial theorem. Minggatu's work is remarkable in that expansions in series, trigonometric and logarithmic were apprehended algebraically and inductively without the aid of differential and integral calculus.
  In 1742 he participated in the revision of the Compendium of Observational and Computational Astronomy. In 1756, he participated in the surveying of the Dzungar Khanate (renamed Xinjiang), which was incorporated into the Qing Empire by the Qianlong Emperor. It was due to his geographical surveys in Xinjiang that the Complete Atlas of the Empire (the first atlas of China drawn with scientific methods) was finished.
  From 1760-1763, shortly before his death, he was administrator of the Imperial Astronomical Bureau.
caption: Ming Antu discovered Catalan numbers
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