mathematics

Minggatu

Minggatu is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Minggatu rather than just read about it. In short: Minggatu (Mongolian script: ᠮᠢᠩᠭᠠᠲᠦ; Chinese: 明安图; pinyin: Míng'āntú, c. 1692 – c. 1763), full name Sharavyn Myangat (Mongolian: Шаравын Мянгат), also known as Ming Antu, was a Mongolian astronomer, mathematician, and topographic scientist at the Qing court. His courtesy name was Jing An (静安).

Key takeaways

Minggatu belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Minggatu to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Minggatu from memory before moving on to harder problems.

Reference excerpt

Minggatu (Mongolian script: ᠮᠢᠩᠭᠠᠲᠦ; Chinese: 明安图; pinyin: Míng'āntú, c. 1692 – c. 1763), full name Sharavyn Myangat (Mongolian: Шаравын Мянгат), also known as Ming Antu, 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 Inner Mongolia 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 to 1763, shortly before his death, he was administrator of the Imperial Astronomical Bureau.

Later recognition In 1910, Japanese mathematician Yoshio Mikami mentioned that Minggatu was the first Mongolian who had ever entered into the field of analytical research methods. Mathematician Dr. P. J. Larcombe of Derby University published seven papers on Minggatu and his work in 1999, including the stimulus of Jesuit missionary, engineer, mathematician and geographer Pierre Jartoux, who brought three infinite series to China early in the 1700s. On May 26, 2002, the minor planet 28242 was named after Minggatu as 28242 Mingantu. The nomination ceremony and traditional meeting were held in Minggatu's hometown in August 2002. More than 500 delegates and 20,000 local residents gathered together to celebrate and a conference on "The Science Contribution of Ming Antu" was held. The Chinese government named Minggatu’s hometown as "Ming Antu Town".

See also Ming Antu's infinite series expansion of trigonometric functions

References

Illustrations

Worked examples

Example 1 — a first encounter with Minggatu

Start with the simplest possible case. Write down what Minggatu claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Minggatu before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Minggatu ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Minggatu

In research: Minggatu appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Minggatu in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Minggatu is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1763 deaths, 18th-century Chinese mathematicians, 18th-century astronomers, so understanding it makes those chapters shorter.
In everyday life: Look for Minggatu outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Minggatu in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Minggatu means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Minggatu out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Minggatu in simple terms?

Why does Minggatu matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Minggatu?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Minggatu.