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 The Han dynasty was an Dynasties of China, imperial dynasty of China (202 BC9 AD, 25–220 AD) established by Liu Bang and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–206 BC ...

, sometime between 202 BC and 186 BC.Liu et al. (2003), 9. It was preserved among the

Zhangjiashan Han bamboo texts The Zhangjiashan Han bamboo texts are ancient Han dynasty Chinese written works dated 196–186 BC. They were discovered in 1983 by archaeologists excavating tomb no. 247 at Mount Zhangjia () of Jiangling County, Hubei Province (near modern Ji ...

and contains similar mathematical problems and principles found in the later

Eastern Han The Han dynasty was an Dynasties of China, imperial dynasty of China (202 BC9 AD, 25–220 AD) established by Liu Bang and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–206 BC ...

period text of ''

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. This book is one of the earliest surviving ...

''.

Discovery

The text was found in tomb M247 of the burial grounds near Zhangjiashan,

Jiangling County Jiangling () is a county in southern Hubei province, People's Republic of China. Administratively, it is under the jurisdiction of Jingzhou City. History The county name derived from the old name of Jingzhou. Liang Dynasty Prince Xiao Yi (蕭繹 ...

, in

Hubei Hubei is a province of China, province in Central China. It has the List of Chinese provincial-level divisions by GDP, seventh-largest economy among Chinese provinces, the second-largest within Central China, and the third-largest among inland ...

province, excavated in December–January 1983–1984. This tomb belonged to an anonymous civil servant in early West Han dynasty. In the tomb were 1200 bamboo strips written in ink. Originally the strips were bound together with string, but the string had rotted away and it took Chinese scholars 17 years to piece together the strips. As well as the mathematical work the strips covered government statutes, law reports and therapeutic gymnastics. On the back of the sixth strip, the top has a black square mark, followed by the three characters 筭數書, which serve as the title of the rolled up book.

Content

The Suàn shù shū consists of 200 strips of

bamboo Bamboos are a diverse group of mostly evergreen perennial plant, perennial flowering plants making up the subfamily (biology), subfamily Bambusoideae of the grass family Poaceae. Giant bamboos are the largest members of the grass family, in th ...

written in ink, 180 strips are intact, the others have rotted. They consist of 69 mathematical problems from a variety of sources, two names Mr Wáng and Mr Yáng were found, probably two of the writers. Each problem has a question, an answer, followed by a method. The problems cover

elementary arithmetic Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and Division (mathematics), division. Due to its low level of abstraction, broad range of application, and position as the foundation of all mathema ...

;

fractions A fraction (from , "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, thre ...

; inverse proportion; factorization of numbers;

geometric progression A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed number called the ''common ratio''. For example, the s ...

s, in particular

interest rate An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, ...

calculations and handling of errors; conversion between different units; the

false position method In mathematics, the ''regula falsi'', method of false position, or false position method is a very old method for solving an equation with one unknown; this method, in modified form, is still in use. In simple terms, the method is the trial and er ...

for finding roots and the extraction of approximate

square root In mathematics, a square root of a number is a number such that y^2 = x; in other words, a number whose ''square'' (the result of multiplying the number by itself, or y \cdot y) is . For example, 4 and −4 are square roots of 16 because 4 ...

s; calculation of the

volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...

of various 3-dimensional shapes; relative dimensions of a

square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

and its inscribed

circle A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...

; calculation of unknown side of rectangle, given area and one side. All the calculations about circumference and area of circle are approximate, equivalent to taking π = 3. Calculations of pi were made more accurate with the work of Liu Xin (c. 46 BC – 23 AD),

Zhang Heng Zhang Heng (; AD 78–139), formerly romanization of Chinese, romanized Chang Heng, was a Chinese polymathic scientist and statesman who lived during the Han dynasty#Eastern Han (25–220 AD), Eastern Han dynasty. Educated in the capital citi ...

(78–139 AD),

Liu Hui Liu Hui () was a Chinese mathematician who published a commentary in 263 CE on ''Jiu Zhang Suan Shu ( The Nine Chapters on the Mathematical Art).'' He was a descendant of the Marquis of Zixiang of the Eastern Han dynasty and lived in the state ...

(fl. 3rd century AD), and

Zu Chongzhi Zu Chongzhi (; 429 – 500), courtesy name Wenyuan (), was a Chinese astronomer, inventor, mathematician, politician, and writer during the Liu Song and Southern Qi dynasties. He was most notable for calculating pi as between 3.1415926 and 3.1415 ...

(429–500). Prior to discovery the oldest Chinese mathematical text were the

Zhoubi Suanjing The ''Zhoubi Suanjing'', also known by many other names, is an ancient Chinese astronomical and mathematical work. The ''Zhoubi'' is most famous for its presentation of Chinese cosmology and a form of the Pythagorean theorem. It claims to pr ...

and ''

'' which dates from around 100 CE. Many topics are covered in both texts, however, error correction problems only appear in the Suàn shù shū, and the last two chapter of the nine chapters have no corresponding material in the Suàn shù shū. The text has been translated to English by Christopher Cullen, director of the Needham Research Institute.The Suan shu shu 筭數書 'Writings on Reckoning'
/ref>

Notes

References

*Christopher Cullen: The Suan shu shu Writings on reckoning, Needham Research Institute, pdf free downloa

* * Dauben, Joseph W. (2004). "The Suan Shu Shu (A Book on Numbers and Computation), A Preliminary Investigation" in ''Form, Zahl, Ordnung'', 151–168. München: Franz Steiner Verlag. . *Dauben, Joseph W. (2007). "Chinese Mathematics" in ''The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook'', 187–384. Edited by Victor J. Katz. Princeton: Princeton University Press. . * Guilin Liu, Lisheng Feng, Airong Jiang, and Xiaohui Zheng. (2003). The Development of E-mathematics Resources at Tsinghua University Library (THUL)," in ''Electronic Information and Communication in Mathematics'', 1–13. Edited by Fengshen Bai and Bernd Wegner. Berlin: Springer. . * Stephanie Pain, ''Histories: China's oldest mathematical puzzles'',

New Scientist ''New Scientist'' is a popular science magazine covering all aspects of science and technology. Based in London, it publishes weekly English-language editions in the United Kingdom, the United States and Australia. An editorially separate organ ...

, 30 July 2006

* Péng Hào, ''Zhāngjiāshān Hànjiǎn "Suàn shù shū" zhùshì (The Hàn dynasty book on wooden strips "Suàn shù shū" found at Zhāngjiāshān with a commentary and explanation)'' Beijing, Science Press, (2001). * Wu Wenjun ed, Zhong Guo Shu Xue Shi Da Xi(The Grand Series of History of Chinese Mathematics) vol 1, chapter 2, "Suan Shu Shu". *Rémi Anicotte (2019). ''Le Livre sur les calculs effectués avec des bâtonnets – Un manuscrit du -IIe siècle excavé à Zhangjiashan'', Paris: Presses de l'Inalco. http://www.inalco.fr/publication/livre-calculs-effectues-batonnets-manuscrit-iie-siecle-excave-zhangjiashan

External links

Full text of book
Christopher Cullen: Suan shu shu ''Writings on reckoning'' Needham Research Institute {{DEFAULTSORT:Book On Numbers And Computation Archaeological artifacts of China Mathematics manuscripts Chinese mathematics texts Han dynasty texts Han dynasty literature 2nd-century BC books Mathematics books