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Book on Numbers and Computation

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TheBook on Numbers and Computation(Chinese:Toán sổ thư;pinyin:Suàn shù shū), or theWritings on Reckoning,[1]is one of the earliest knownChinese mathematical treatises.It was written during the early WesternHan dynasty,sometime between 202 BC and 186 BC.[2]It was preserved among theZhangjiashan Han bamboo textsand contains similar mathematical problems and principles found in the laterEastern Hanperiod text ofThe Nine Chapters on the Mathematical Art.

Discovery

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The text was found in tomb M247 of the burial grounds nearZhangjiashan,Jiangling County,inHubeiprovince, excavated in December–January 1983–1984.[2][3]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 toán sổ thư,[4][5]which serve as the title of the rolled up book.

Content

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The Suàn shù shū consists of 200 strips ofbamboowritten 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 coverelementary arithmetic;fractions;inverse proportion; factorization of numbers;geometric progressions,in particularinterest ratecalculations and handling of errors; conversion between different units; thefalse position methodfor finding roots and the extraction of approximatesquare roots;calculation of thevolumeof various 3-dimensional shapes; relative dimensions of asquareand its inscribedcircle;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 ofLiu Xin(c. 46 BC – 23 AD),Zhang Heng(78–139 AD),Liu Hui(fl. 3rd century AD), andZu Chongzhi(429–500).

Prior to discovery the oldest Chinese mathematical text were theZhoubi SuanjingandThe Nine Chapters on the Mathematical Artwhich 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 byChristopher Cullen,director of theNeedham Research Institute.[6]

Notes

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  1. ^Dauben (2004), 151.
  2. ^abLiu et al. (2003), 9.
  3. ^Dauben (2007), 201.
  4. ^Cullen, p117
  5. ^Cullen, Christopher (2007)."The Suàn shù shū," Writings on reckoning ": Rewriting the history of early Chinese mathematics in the light of an excavated manuscript".Historia Mathematica.34:10–44.doi:10.1016/j.hm.2005.11.006.
  6. ^The Suan shu shu toán sổ thư 'Writings on Reckoning'

References

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