Suan Shu Shu

The Suàn shù shū ( Chinese 算數書 - "arithmetic and numerical book") is the earliest Chinese text on mathematics. The text was written in the early Western Han Dynasty between 202 and 186 BC. Written on bamboo strips ( Chinese 竹简 ). His discovery rewrote the history of Chinese mathematics, as the text is about 300 years older than the “ Nine Chapters of Arithmetic ” ( Chinese 九章算術 ).

Discovery and Publication

The text was found and excavated on a burial ground with others in the M247 tomb near Zhangjiashan 张家山, Jiangling District , Hubei in 1984 . The tomb belonged to an anonymous official from the early Western Han Dynasty. Apart from the Suan Shu Shu , a total of 1200 bamboo strips written with Indian ink and tied with three strings were found. However, over the years these had rotten and the chopsticks mixed up. In 17 years of work, Chinese scientists put these together again in meticulous work, and in 2000 an edition in abbreviations was published for the first time in the journal Wenwu文物.

Form and content

In addition to the other texts on the found bamboo sticks, the Suan Shu Shu includes 200 bamboo strips, 180 of which have been preserved. The text, about 7000 characters long, is undated and anonymous and written in the Lìshū . There are 3 to 36 characters on each strip. Below some bamboo joints is the sign “Wáng 王” or “Yáng 杨”; on some of the complete stripes it says “Wang has tested it” ( Chinese 王已讎 , Pinyin Wáng yǐ chóu ), “Yang has tested it” ( Chinese 杨已讎 , Pinyin Yáng yǐchóu ). This means that possibly two with the surname Wang and Yang both corrected this text for errors and copied it. 69 mathematical problems are the core content of Suan Shu Shu , which are built up using a question, answer and concluding method (shù 術). They include the following problems: basic arithmetic operations , fractions , anti- proportionality ( inverse proportionality ) , decomposition of factors , sequences and series , in particular interest rate calculations and their troubleshooting, conversions between units of measurement, rule-falsi method, calculation of volumes of various bodies, relative dimensions of a square with a drawn in Circle, calculation of the unknown side of a rectangle. All calculations for the circumference and area are made with a rounding of the number π = 3. Only through Liu Xin († 23 AD), Zhang Heng (78-139), Liu Hui (3rd century AD), and Zu Chongzhi (429-500) was an increased accuracy of the number pi achieved .

Before the discovery of the text, the oldest mathematical treatises were the Zhoubi suanjing and the Jiu Zhang Suan Shu (九章算術), which dates from around 100 BC. Were created. With the discovery of Suan Shu Shu , the history of mathematics in China was given an even earlier work, around 300 years older. The comparative research on the Jiu Zhang Suan Shu and the Suan Shu Shu has been a controversial field since the discovery: Since both the language style, the units of measurement as well as the mathematical problems and solution approaches in both texts are similar, the Suan Shu Shu is used as one of the templates for the Jiu Zhang Suan Shu edited by Zhang Can 張倉.

The Suan Shu Shu itself was translated into English by Christopher Cullen , director of the Needham Institute.

literature

Christopher Cullen: The Suan Shu Shu Image, “Writings on reckoning”: Rewriting the history of early Chinese mathematics in the light of an excavated manuscript . In: Historia Mathematica , Volume 34, 2007, pp. 10-44 doi : 10.1016 / j.hm.2005.11.006

Joseph W. Dauben : The Suan Shu Shu (A Book on Numbers and Computation), A Preliminary Investigation . In: Form, number, order , Franz Steiner Verlag, Munich 2004, ISBN 3-515-08525-4 , pp. 151–168.

Joseph W. Dauben Suan Shu Shu, a book on numbers and computations: English translation with commentary , Archive for the History of Exact Sciences, Volume 62, 2008, pp. 91-178, 347

Guilin Liu, Lisheng Feng, Airong Jiang, Xiaohui Zheng: The Development of E-mathematics Resources at Tsinghua University Library (THUL) . In: Fengshen Bai, Bernd Wegner (eds.): Electronic Information and Communication in Mathematics , Springer, Berlin 2003, ISBN 3-540-40689-1 , pp. 1-13.

Stephanie Pain: Histories: China's oldest mathematical puzzles . In: New Scientist , July 30, 2006, newscientist.com

彭浩《张家山汉简算数书注释》, 北京：科学出版社, 2001 年 [Peng Hao, annotated edition of the hanzeit bamboo text "Suan Shu Shu" by Zhangjiashan . Science Publishing, Beijing 2001].

吴文俊主编《中国数学史大系》副卷, 沈康身编《算数书解说》副卷第一卷, 1-16 、 41-71 、 81-116 、 120-275 、 277-290 页，北京师范大学出版社, 1998 年, ISBN 7-303-04555-4 [Shen, Kangshen: Explanations of Suan Shu Shu . In: Wu, Wenjun (Ed.), Compendium on the History of Mathematics of China . University of Education Publishers , Beijing 1998, ISBN 7-303-04555-4 , pages 1-16, 41-71, 81-116, 120-275, 277-290].

swell

↑ Liu et al. (2003), 9.
↑ Liu et al. (2003), 9.
↑ 江陵張家山漢簡整理小組《江陵張家山漢簡〈算數書〉釋文》 ( Suan Shu Shu , hanzeit text on bamboo strips, Jiangling district, Zhangjiashan) 《文物》 2000 年 9 月 78-84 頁。
↑ Original title: 里田，約分，合分，出金，徑分，分當半者，增減分，乘，，相乘，分乘，大廣，粺穀，粟求米，米求粟，粟為米，粟求米，春粟，取程，耗，耗租，程禾，絲練，羽矢，，取枲程，程竹，，挐脂，銅耗，金價，漆錢，飲，石，醫，賈鹽，米粟並，粟米並，並租，女織，婦織，狐皮，狐出關關，傳馬，共買材材，稅田，誤帣，租誤帣，繒幅，息錢錢錢錢錢少廣，少廣，啟廣，啟從，圓材，井材，圓亭，除，鄆都，，芻，旋粟，囷囷蓋，負炭，羽矢，盧唐，負米，出，米米米米米米錢，方田，以方材圓，以圓材方，形。

Web links

Full text version of the Needham Research Institute

[1] Liu et al. (2003), 9.

[2] Liu et al. (2003), 9.

[3] 江陵張家山漢簡整理小組《江陵張家山漢簡〈算數書〉釋文》 ( Suan Shu Shu , hanzeit text on bamboo strips, Jiangling district, Zhangjiashan) 《文物》 2000 年 9 月 78-84 頁。

[4] Original title: 里田，約分，合分，出金，徑分，分當半者，增減分，乘，，相乘，分乘，大廣，粺穀，粟求米，米求粟，粟為米，粟求米，春粟，取程，耗，耗租，程禾，絲練，羽矢，，取枲程，程竹，，挐脂，銅耗，金價，漆錢，飲，石，醫，賈鹽，米粟並，粟米並，並租，女織，婦織，狐皮，狐出關關，傳馬，共買材材，稅田，誤帣，租誤帣，繒幅，息錢錢錢錢錢少廣，少廣，啟廣，啟從，圓材，井材，圓亭，除，鄆都，，芻，旋粟，囷囷蓋，負炭，羽矢，盧唐，負米，出，米米米米米米錢，方田，以方材圓，以圓材方，形。