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 mathematicaltreatise written during 3rd to 5th centuries CE which was listed as one of theTen Computational Canons during theTang dynasty. The specific identity of its author Sunzi (lit. "Master Sun") is still unknown but he lived much later than his namesakeSun Tzu, author ofThe Art of War. From the textual evidence in the book, some scholars concluded that the work was completed during theSouthern and Northern Dynasties.[2] Besides describing arithmetic methods and investigatingDiophantine equations, the treatise touches uponastronomy and attempts to develop acalendar.[citation needed]
The book is divided into three chapters.
Chapter 1 discusses measurement units of length, weight and capacity, and the rules ofcounting rods. Although counting rods were in use in theSpring and Autumn period and there were many ancient books on mathematics such asBook on Numbers and Computation andThe 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",[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 deals with operational rules for fractions with rod numerals: the reduction, addition, subtraction, and division of fractions, followed by mechanical algorithm for theextraction of square roots.[4]
Chapter 3 contains the earliest example of theChinese remainder theorem, a key tool to understanding and resolvingDiophantine equations.
Researchers have published a full English translation of theSūnzĭ Suànjīng:
The original Chinese text is available on Wikisource.
