mathematics

Sunzi Suanjing

Sunzi Suanjing 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 Sunzi Suanjing rather than just read about it. In short: Sunzi Suanjing (Chinese: 孫子算經; pinyin: Sūnzǐ Suànjīng; Wade–Giles: Sun Tzu Suan Ching; lit. 'The Mathematical Classic of Master Sun/Master Sun's Mathematical Manual') was a mathematical treatise written during 3rd to 5th centuries CE which was listed as one of the Ten Computational Canons during the Tang dynasty. The specific identity of its author Sunzi (lit. "Master Sun") is still unknown but he lived much later t…

Key takeaways

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

Reference excerpt

Sunzi Suanjing (Chinese: 孫子算經; pinyin: Sūnzǐ Suànjīng; Wade–Giles: Sun Tzu Suan Ching; lit. 'The Mathematical Classic of Master Sun/Master Sun's Mathematical Manual') was a mathematical treatise written during 3rd to 5th centuries CE which was listed as one of the Ten Computational Canons during the Tang dynasty. The specific identity of its author Sunzi (lit. "Master Sun") is still unknown but he lived much later than his namesake Sun Tzu, author of The Art of War. From the textual evidence in the book, some scholars concluded that the work was completed during the Southern and Northern Dynasties. Besides describing arithmetic methods and investigating Diophantine equations, the treatise touches upon astronomy and attempts to develop a calendar.

Contents

The book is divided into three chapters.

Chapter 1 Chapter 1 discusses measurement units of length, weight and capacity, and the rules of counting rods. Although counting rods were in use in the Spring and Autumn period and there were many ancient books on mathematics such as Book on Numbers and Computation and The Nine Chapters on the Mathematical Art, no detailed account of the rules was given. For the first time, The Mathematical Classic of Sun Zi provided a detail description of the rules of counting rods: "one must know the position of the counting rods, the units are vertical, the tens horizontal, the hundreds stand, the thousands prostrate", followed by the detailed layout and rules for manipulation of the counting rods in addition, subtraction, multiplication, and division with ample examples.

Chapter 2 Chapter 2 deals with operational rules for fractions with rod numerals: the reduction, addition, subtraction, and division of fractions, followed by mechanical algorithm for the extraction of square roots.

Chapter 3 Chapter 3 contains the earliest example of the Chinese remainder theorem, a key tool to understanding and resolving Diophantine equations.

References

Bibliography Researchers have published a full English translation of the Sūnzĭ Suànjīng:

Fleeting Footsteps; Tracing the Conception of Arithmetic and Algebra in Ancient China, by Lam Lay Yong and Ang Tian Se, Part Two, pp 149–182. World Scientific Publishing Company; June 2004 ISBN 981-238-696-3 The original Chinese text is available on Wikisource.

External links Sun Zi at MacTutor

Illustrations

Worked examples

Example 1 — a first encounter with Sunzi Suanjing

Start with the simplest possible case. Write down what Sunzi Suanjing 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 Sunzi Suanjing 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 Sunzi Suanjing 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 Sunzi Suanjing

In research: Sunzi Suanjing 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 Sunzi Suanjing 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: Sunzi Suanjing is common in secondary-school and first-year university syllabi. It links to neighbouring topics Chinese mathematics texts, Northern and Southern dynasties literature, so understanding it makes those chapters shorter.
In everyday life: Look for Sunzi Suanjing 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 Sunzi Suanjing in 20 minutes

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

Frequently asked questions

What is Sunzi Suanjing in simple terms?

Why does Sunzi Suanjing 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 Sunzi Suanjing?

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 Sunzi Suanjing.