''Sunzi Suanjing'' () was a mathematical

treatise A treatise is a formal and systematic written discourse on some subject, generally longer and treating it in greater depth than an essay, and more concerned with investigating or exposing the principles of the subject and its conclusions." Tre ...

written during 3rd to 5th centuries AD which was listed as one of the Ten Computational Canons during the

Tang dynasty The Tang dynasty (, ; zh, t= ), or Tang Empire, was an imperial dynasty of China that ruled from 618 to 907 AD, with an interregnum between 690 and 705. It was preceded by the Sui dynasty and followed by the Five Dynasties and Ten Kingdom ...

. The specific identity of its author Sunzi (lit. "Master Sun") is still unknown but he lived much later than his namesake

Sun Tzu Sun Tzu ( ; zh, t=孫子, s=孙子, first= t, p=Sūnzǐ) was a Chinese military general, strategist, philosopher, and writer who lived during the Eastern Zhou period of 771 to 256 BCE. Sun Tzu is traditionally credited as the author of '' The ...

, author of ''

The Art of War ''The Art of War'' () is an ancient Chinese military treatise dating from the Late Spring and Autumn Period (roughly 5th century BC). The work, which is attributed to the ancient Chinese military strategist Sun Tzu ("Master Sun"), is com ...

''. From the textual evidence in the book, some scholars concluded that the work was completed during the

Southern and Northern Dynasties The Northern and Southern dynasties () was a period of political division in the history of China that lasted from 420 to 589, following the tumultuous era of the Sixteen Kingdoms and the Eastern Jin dynasty. It is sometimes considered as ...

. Besides describing arithmetic methods and investigating Diophantine equations, the treatise touches upon

astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...

and attempts to develop a calendar.

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 Counting rods () are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number. The written ...

. 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 The ''Book on Numbers and Computation'' (), or the ''Writings on Reckoning'', is one of the earliest known Chinese mathematical treatises. It was written during the early Western Han dynasty, sometime between 202 BC and 186 BC.Liu et al. (2003), ...

'' and ''

The Nine Chapters on the Mathematical Art ''The Nine Chapters on the Mathematical Art'' () is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE. This book is one of the earliest sur ...

'', 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. Lam Lay Yong and An Tian Se, Fleeting Footsteps p65, ''World Scientific'',

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 The original Chinese text is available on Wikisource.

External links

Sun Zi at MacTutor

References