Book on Numbers and Computation

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Book on Numbers and Computation

Post  msistarted on Tue Oct 26, 2010 11:22 pm

The Sun sh shū (筭數書), or the Writings on Reckoning (also as Book on Numbers and Computation),[1] is one of the earliest known Chinese mathematical treatises. It was written during the early Western Han Dynasty, sometime between 202 BC and 186 BC.[2]
Contents [hide]
1 Discovery
2 Content
3 Notes
4 References
5 External links

The text was found in tomb M247 of the burial grounds near Zhangjiashan, Jiangling County, in Hubei province, excavated in DecemberJanuary of 19831984.[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 #6 strip, the top has a black square mark,followed by three characthers 筭數書[1],[4] which served as title of the rolled up book.

The Sun sh 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 Wng and Mr Yng 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 23 AD), Zhang Heng (78139 AD), Liu Hui (fl. 3rd century AD), and Zu Chongzhi (429500).
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 Sun sh shū, and the last two chapter of the nine chapters have no corresponding material in the Sun sh shū.
The text has been translated to English by Christopher Cullen director of the Needham Research Institute

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