Mathematics in China (original) (raw)
Number System and Calculation Tools
Archaeologic finds from the Shang dynasty (fourteenth to eleventh century BCE) show the earliest number symbols inscribed on bones and tortoise shells. By then, different decimal and sexagesimal systems were in use. The use of rod‐numerals is also attested on coins as early as from the Wang Mang period (9–23 AD). These are related to the instruments in use. For calculations, numbers were represented on a calculation surface by counting rods. The representation follows a decimal positional notation, where nine different signs for the numbers from 1 to 10 consist of either vertical or horizontal bars used to mark units, hundreds, myriads, etc. or tens, thousands, and other odd powers of ten. Three hundred twenty‐six for example was thus put down in the following way: III = T. For negative numbers, black instead of red counting rods were used. In printed records (from the eleventh century onwards) they were marked by an oblique bar (Fig. 1).
Fig. 1
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References
Editions of Primary Sources and Reprints
- Guo, Shuchun, ed. Zhongguo kexue jishu dianji tonghui: Shuxue juan. A Compendium of Chinese Classics of Science and Technology: Mathematics Section. 5 vols. Zhenzhou: Henan jiaoyu chubanshe, 1993.
Google Scholar - Jing, Yushu, ed. Zhongguo lidai suanxue jicheng. Collected Chinese Mathematical Texts from all Dynasties. 4 vols. Jinan: Shandong jiaoyu chubanshe, 1994.
Google Scholar - Peng, Hao. Zhangjiashan Hanjian «Suan Shu Shu» zhushi. Commentary and Explanations on the «Suan Shu Shu» Han dynasty bamboo slips unearthed from Zhangjiashan. Beijing: Kexue chubanshe, 2001.
Google Scholar
Secondary Sources
- Bréard, Andrea. Re‐Kreation eines mathematischen Konzeptes im chinesischen Diskurs: Reihem vom 1. bis zum 19. Jahrhundert. Stuttgart: Steiner, 1999.
Google Scholar - ‐‐‐. On Mathematical Terminology. Culture Crossing in Nineteenth‐Century China. http://www.wsc.uni‐erlangen.de/pdf/breard.pdf.
- Bréard, Andrea, Joseph Dauben, and Xu Yibao. The History of Chinese Mathematics: The Past 25 Years. ILULL 26 (2003): 429–74.
Google Scholar - Cullen, Christopher. Astronomy and Mathematics in Ancient China: The Zhou bi suan jing. Needham Research Institute Studies; 1. Cambridge: Cambridge University Press, 1996.
Google Scholar - Dauben, Joseph W. Mathematics, Ideology, and the Politics of Infinitesimals: Mathematical Logic and Nonstandard Analysis in Modern China. History & Philosophy of Logic 24(4) (2003): 327–63.
Google Scholar - Du, Shiran, Guo Shuchun, and Liu Dun, ed. Li Yan Qian Baocong kexue shi quanji. Complete Works in the History of Science by Li Yan and Qian Baocong. 10 vols. Shenyang: Liaoning jiaoyu chubanshe, 1998.
Google Scholar - Engelfriet, Peter M. Euclid in China: The Genesis of the First Chinese Translation of Euclid's Elements Books I–VI (Jihe yuanben; Beijing, 1607) and its reception up to 1723. Sinica Leidensia. Vol. 40. Leiden: Brill, 1998.
Google Scholar - Hart, Roger. Quantifying Ritual: Political Cosmology, Courtly Music, and Precision Mathematics in Seventeenth‐Century China. http://uts.cc.utexas.edu/∼rhart/papers/quantifying.html.
- Horng, Wann‐sheng, Li Shanlan, the Impact of Western Mathematics in China during the Late 19th Century. PhD Thesis. City University, New York, NY, 1991.
Google Scholar - ‐‐‐. Tantian sanyou (Three Chatting Friends). Taipei: Mingwen shuju, 1993.
Google Scholar - Jami, Catherine. Les méthodes rapides pour la trigonométrie et le rapport précis du cercle (1774). Tradition chinoise et apport occidental en mathématiques. Mémoires de l'Institut des Hautes Études Chinoises; XXXII. Paris: Collège de France, 1990.
Google Scholar - Lam, Lay Yong. A critical study of the ‘Yang Hui suan fa': a thirteenth century mathematical treatise. Singapore: Singapore University Press, 1977.
Google Scholar - Lam, Lay Yong and Ang Tian Se. Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China. Singapore: World Scientific Publishing, 1992.
Google Scholar - Li, Di. Zhongguo shuxue shi jianbian. A Brief History of Chinese Mathematics. Shenyang: Liaoning renmin chubanshe, 1984.
Google Scholar - ‐‐‐. Zhongguo shuxue shi. A History of Chinese Mathematics. 4 vols. Nanjing: Jiangsu jiaoyu chubanshe, 1997.
Google Scholar - Li, Zhaohua. Zhongguo shuxue shi. A History of Chinese Mathematics. Taibei: Wenjing chubanshe, 1995.
Google Scholar - Li, Yan and Du Shiran. Chinese Mathematics: A Concise History. Oxford: Clarendon Press, 1987.
Google Scholar - Libbrecht, Ulrich. Chinese Mathematics in the Thirteenth Century. Cambridge, MA: MIT Press, 1973.
Google Scholar - Liu, Dun. Da zai yan shu. Great to Talk About Mathematics. Shenyang: Liaoning jiaoyu chubanshe, 1993.
Google Scholar - Mac Lane, Saunders. Pure and Applied Mathematics. Science in contemporary China. Ed. Leo A. Orleans. Stanford, CA: Stanford University Press, 1980. 53–83.
Google Scholar - Martzloff, Jean‐Claude. A History of Chinese Mathematics. Berlin Heidelberg New York: Springer, 1997.
Google Scholar - Mei, Rongzhao, ed. Ming Qing shuxueshi lunwenji. Collected Papers on the History of Mathematics during the Ming and Qing Dynasties. Nanjing: Jiangsu jiaoyu chubanshe, 1990.
Google Scholar - Qian, Baocong, ed. Song Yuan shuxue shi lunwenji. Collected Papers on the History of Mathematics During the Song and Yuan Dynasties. Beijing: Kexue chubanshe, 1966.
Google Scholar - Shen, Kangshen. Zhongsuan daolun. An Introduction to Chinese Mathematics. Shanghai: Shanghai jiaoyu chubanshe, 1986.
Google Scholar - Wang, Yusheng and Liu Dun, ed. Zhongguo shuxue shi daxi. Comprehensive Series on the History of Chinese Mathematics. Shijiazhuang: Heibei kexue jishu chubanshe, 2000.
Google Scholar - Wu, Wenjun, ed. 1985. –1996 Zhongguo shuxue shi lunwenji. Collected Papers on the History of Chinese Mathematics. 6 issues. Jinan: Shandong jiaoyu chubanshe, (Sixth issue Ed. Bai, Shangshu, Li Di, and Shen Kangshen).
Google Scholar - ‐‐‐. Zhongguo shuxue shi daxi. Comprehensive Series on the History of Chinese Mathematics. 10 vols. Beijing: Beijing shifan daxue chubanshe, 1998. (Vol. I: Shanggu dao Xi Han. From Prehistoric Times to the Western Han. Ed. Li Di, 1998; Vol. II: Zhongguo gudai shuxue mingzhu Jiu zhang suan shu. The Ancient Chinese Mathematical Classic: The Nine Chapters on Mathematical Procedures. Ed. Shen Kangshen, 1998; Dong Han San Guo. Eastern Han and Three Kingdoms. Ed. Bai Shangshu, 1998; Xi Jin zhi Wu Dai. From Western Jin to the Five Dynasties. Ed. Shen Kangshen, 1999; Liang Song. The Two Song Dynasties. Ed. Shen Kangshen, 2000; Xi Xia Jin Yuan Ming. Western Xia, Jin, Yuan and Ming Dynasties. Ed. Li Di, 1999; Mingmo dao Qing zhongqi. From the End of the Ming Dynasty to the Mid‐Qing Period. Ed. Li Di, 2000; Qing zhongqi dao Qing mo. From the Mid‐Qing Period to the End of the Qing Dynasty. Ed. Li Zhaohua, 2000; Zhongguo suanxue shumu huibian. Bibliography of Traditional Chinese Mathematical Texts. Ed. Li Di, 2000).
Google Scholar
Authors
- Andrea Eberhard‐Bréard
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- Hampshire College, 893 West Street, 01002, Amherst, MA, USA
Helaine Selin (Editor) (Editor)
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