The Mathematical Classic of Sun Zi
(Sunzi Suanjing, 孙子算经) was a mathematical treatise written during the 5th century, and was listed as one of The Ten Computational Canons
The Ten Computational Canons is a collection of Chinese mathematical works, compiled by early Tang dynasty mathematician Li Chunfeng The Ten Computational Canons is a collection of Chinese mathematical works, compiled by early Tang dynasty mathematician Li Chunfeng The Ten Computational Canons is a...
in Tang Dynasty
The Tang Dynasty was an imperial dynasty of China preceded by the Sui Dynasty and followed by the Five Dynasties and Ten Kingdoms Period. It was founded by the Li family, who seized power during the decline and collapse of the Sui Empire...
. The identity of the author Sunzi is still unknown, and not to be confused with the author of The Art of War
The Art of War is an ancient Chinese military treatise that is attributed to Sun Tzu , a high ranking military general and strategist during the late Spring and Autumn period...
. From the textual evidence in the book, some scholars concluded that the work was completed during the Southern and Northern Dynasties
The Southern and Northern Dynasties was a period in the history of China that lasted from 420 to 589 AD. Though an age of civil war and political chaos, it was also a time of flourishing arts and culture, advancement in technology, and the spreading of Mahayana Buddhism and Daoism...
, for instance, in problem 33, of vol 3, there is a sentence "Luoyang is 900 li away from Chang An, as Chang An first showed up in Han Dynasty
The Han Dynasty was the second imperial dynasty of China, preceded by the Qin Dynasty and succeeded by the Three Kingdoms . It was founded by the rebel leader Liu Bang, known posthumously as Emperor Gaozu of Han. It was briefly interrupted by the Xin Dynasty of the former regent Wang Mang...
, hennce this work cannot be written before 3thd century. Also in problem 3 of vol 3, there is a ssentence:
We have a board game, 19 rows and 19 columns sqauare, question, how many stones are there ?", since Go (game) made its first aappearance in mid 3rd century, hence the work was most probably written during the Wei and Jin Dynasties.
The book is divided into three chapters:
Chapter 1: Detailed discussion on measurement units of length, weight and capacity, and the rules of counting rods
Counting rods are small bars, typically 3–14 cm long, used by mathematicians for calculation in China, Japan, Korea, and Vietnam. They are placed either horizontally or vertically to represent any number and any fraction....
. 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, 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 1st century CE...
, 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". Followed by the detailed laymout and rules for manipulation of the counting rods in addition, subtraction,multiplication and division with ample examples.
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.
Chapter 3 contains the earliest example of Chinese remainder theorem
The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra.In its most basic form it concerned with determining n, given the remainders generated by division of n by several numbers...
There is a full translation of The Mathematical Classic of Sun Zi, by Lam Lay Yong
Lam Lay Yong , granddaughter of Tan Kah Kee, niece of Lee Kong Chian, is Professor in Mathematics at the Department of Mathematics, National University of Singapore. She graduated from the National University of Singapore in 1957 and pursued graduate study in Cambridge University, obtaining her Ph.D...
and Ang Tian Se in Tracing the Conception of Arithmetic and Algebra in Ancient China FLEETING FOOTSTPS, Translation of Sun zi Suanjing