mathematics

Li Shanlan

Li Shanlan 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 Li Shanlan rather than just read about it. In short: Li Shanlan (李善蘭, courtesy name: Renshu 壬叔, art name: Qiuren 秋紉) (1810 – 1882) was a Chinese mathematician of the Qing Dynasty. A native of Haining, Zhejiang, he was fascinated by mathematics since childhood, beginning with the Nine Chapters on Mathematical Art.

Key takeaways

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

Reference excerpt

Li Shanlan (李善蘭, courtesy name: Renshu 壬叔, art name: Qiuren 秋紉) (1810 – 1882) was a Chinese mathematician of the Qing Dynasty. A native of Haining, Zhejiang, he was fascinated by mathematics since childhood, beginning with the Nine Chapters on Mathematical Art. He eked out a living by being a private tutor for some years before fleeing to Shanghai in 1852 to evade the Taiping Rebellion. There he collaborated with Alexander Wylie, Joseph Edkins, and others to translate many Western mathematical works into Chinese, including Elements of Analytical Geometry and the Differential and Integral Calculus by Elias Loomis, Augustus De Morgan's Elements of Algebra, and the last nine volumes of Euclid's Elements (from Henry Billingsley's edition), the first six volumes of which having been rendered into Chinese by Matteo Ricci and Xu Guangqi in 1607. With Wylie, he also translated Outlines of Astronomy by John Herschel and coined the Chinese names for many of the low-numbered asteroids. Li coined a great number of mathematical terms that are still used in Chinese today and that were later borrowed into the Japanese language as well. He discovered the Li Shanlan identity (Li Shanlan's summation formulae) in 1867. Later he worked in the think tank of Zeng Guofan. In 1868, he began to teach in Tongwen Guan where he collaborated closely with linguist John Fryer.

Illustrations

Worked examples

Example 1 — a first encounter with Li Shanlan

Start with the simplest possible case. Write down what Li Shanlan 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 Li Shanlan 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 Li Shanlan 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 Li Shanlan

In research: Li Shanlan 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 Li Shanlan 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: Li Shanlan is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1810 births, 1882 deaths, 19th-century Chinese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Li Shanlan 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 Li Shanlan in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Li Shanlan 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 Li Shanlan out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Li Shanlan in simple terms?

Why does Li Shanlan 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 Li Shanlan?

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 Li Shanlan.