Computation: Chinese Counting Rods

  • Lam Lay Yong
Reference work entry

The basic questions in the study of arithmetic in any civilization are: how did the people add, subtract, multiply, and divide, and what were the notations and media that were used to perform these operations.

The ancient Chinese used bamboo sticks or animal bones to count. The first five numbers were tallies in the following form:

The representations for six, seven, eight, and nine were as follows:

The horizontal rod represented the quantity five.

It is easy to imagine how these rod numerals were handled for the addition or subtraction of small numbers such as two plus five or nine minus two. In the case of the addition of, for example, six and seven, the three vertical rods were grouped together and the two horizontal rods representing two fives were replaced by a single rod positioned horizontally to the left of the three vertical rods. The sum, thirteen, was expressed in the following form:

In this manner, a place value notation was created; the tens’ place was to the left of the...

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  1. Crossley, John N. and Alan S. Henry. Thus Spake al‐Khwārizimī: A Translation of the Text of Cambridge University Library Ms. Historia Mathematica 17(1990): 103–31.Google Scholar
  2. Lam Lay Yong. Linkages: Exploring the Similarities Between the Chinese Rod Numeral System and Our Numeral System. Archive for History of Exact Sciences 37 (1987): 365–92.Google Scholar
  3. ‐‐‐. A Chinese Genesis: Rewriting the History of Our Numeral System. Archive for History of Exact Sciences 38 (1988): 101–8.Google Scholar
  4. Lam Lay Yong and Ang Tian Se. Fleeting Footsteps. Tracing the Conception of Arithmetic and Algebra in Ancient China. Singapore: World Scientific, 1992.Google Scholar
  5. Li Yan and Du Shiran. Chinese Mathematics. A Concise History. Trans. by J. N. Crossley and A. W. C. Lun. Oxford: Clarendon Press, 1987.Google Scholar
  6. Mei Rongzhao. The Decimal Place‐Value Numeration and the Rod and Bead Arithmetics. Ancient China's Technology and Science. Beijing: Foreign Languages Press, 1983. 57–65.Google Scholar
  7. Needham, Joseph. Science and Civilisation in China. Vol. 3. Mathematics and the Science of the Heavens and the Earth. Cambridge: Cambridge University Press, 1959.Google Scholar
  8. Qian Baocong, ed. Suan jing shi shu (Ten Mathematical Classics). Beijing: Zhong hua shu ju, 1963.Google Scholar
  9. Saidan, A. S. The Arithmetic of Al‐Uqlīdisī. Dordrecht: D. Reidel, 1978.Google Scholar

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© Springer-Verlag Berlin Heidelberg New York 2008

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  • Lam Lay Yong

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