# Sunzi Suanjing

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Facsimile of Qing dynasty edition of The Mathematical Classic of Sun Zi

Sunzi Suanjing (Chinese: 孙子算经; pinyin: Sūnzĭ Suànjīng; Wade–Giles: Sun Tzu Suan Ching; literally: 'The Mathematical Classic of Master Sun/Master Sun's Mathematical Manual') was a mathematical treatise written during 3rd to 5th centuries AD 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 eponymous 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.[2] Besides describing arithmetic methods and investigating Diophantine equations, the treatise touches upon astronomy and attempts to develop a calendar.[citation needed]

## Contents

Sunzi division algorithm of 6561/9
Al Khwarizimi division identical to Sunzi division
Sunzi square root algorithm
Kushyar ibn Labban division, identical to Sunzi

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 many ancient books on mathematics such as Book on Numbers and Computation and The Nine Chapters on the Mathematical Art, but no detail account of the rules were 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".[3] 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 root.[4]

### Chapter 3

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

## 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.