# Book on Numbers and Computation

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Book on Numbers and Computation

The "Suàn shù shū" (算數書), or the "Book on Numbers and Computation" (also as "Writings on Reckoning"), [Dauben (2004), 151.] is the earliest known Chinese mathematical treatise. It was written during the early Western Han Dynasty, sometime between 202 BC and 186 BC.Liu et al. (2003), 9.]

Discovery

The text was found in tomb M247 of the burial grounds near Zhangjiashan, Jiangling County, in Hubei province excavated in 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.

Content

The Suàn shù shū consists of 200 strips of bamboo 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; fractions;inverse proportion; factorization of number; geometric progressions, in particular interest rate calculations and handling of errors; conversion between different units; the false position method for finding roots and the extraction of approximate square roots; calculation of the volume of various 3-dimensional shapes; relative dimensions of a square and its inscribed circle; 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 &ndash; 23 AD), Zhang Heng (78&ndash;139 AD), Liu Hui (fl. 3rd century AD), and Zu Chongzhi (429&ndash;500).

Prior to discovery the oldest Chinese mathematical text were the Chou Pei Suan Ching and the "The Nine Chapters on the Mathematical Art" 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.

Notes

References

* Christopher Cullen, "The Suàn shù shū Image, “Writings on reckoning”: Rewriting the history of early Chinese mathematics in the light of an excavated manuscript", Historia Mathematica, in Press (2006). [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WG9-4JMKWR7-1&_user=1495569&_handle=V-WA-A-W-BA-MsSAYWW-UUA-U-AACCUWEABW-AACWZUEEBW-EYYEBACBB-BA-U&_fmt=summary&_coverDate=04%2F03%2F2006&_rdoc=12&_orig=browse&_srch=%23toc%236817%239999%23999999999%2399999!&_cdi=6817&view=c&_acct=C000053194&_version=1&_urlVersion=0&_userid=1495569&md5=dd947333736a794d8f3ce0df7e358214]

*Dauben, Joseph W. (2004). "The Suan Shu Shu (A Book on Numbers and Computation), A Preliminary Investigation" in "Form, Zahl, Ordnung", 151&ndash;168. München: Franz Steiner Verlag. ISBN 3515085254.

* 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&ndash;13. Edited by Fengshen Bai and Bernd Wegner. Berlin: Springer. ISBN 3540406891.

* Stephanie Pain, "Histories: China's oldest mathematical puzzles", New Scientist, 30 July 2006. [http://www.newscientist.com/article/mg19125621.800.html]

* 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". ISBN 7-303-04555-4

* [http://www.nri.org.uk/suanshushu.html Full text of book] Needham Research Institute

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