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By Gutierrez J., Shpilrain V., Yu J.-T. (eds.)

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Taylor, Theory and Applications of Numerical Analysis, Academic Press, 1973. f Mathematics. (aporc. Singapore 0511. Republic oj Singapore AND ANG TiAN-SE Department of Chinese Studies. University of Malaya. Kuala Lumpur. Malaysia This paper discusses the method of Liu Hui (3rd century) for evaluating the ratio of the circumfcrcncc ora circle to its diamctcr. now known as 17. A translation of Liu's method is given in the Appendix. Also examined are the values for 17 given by Zu Chongzhi (429-500) and unsurpassed for a millenium.

Historia Mathematica 12, 219-228. Li Di [bg]. 1962. Da kexuejia Zu Chongzhi [ct] [The great scientist Zu Chongzhi]. Shanghai: Renmin chubanshe. ---lbgJ. 1982. Jiu zhang suanshu zhengming wentide gai shu [cuJ [A summary of the various views on the Jiu zhang suanshuJ. , pp. 28-50. Beijing: Shifan daxue chubanshe. Mikami, Y. 1913. The development of mathematics in China and Japan. All page references are to the second edition, New York: Chelsea, 1974. Needham, J. 1959. Science and civilisation in China.

14 + y. 14 + ToX, resulting in x = ir; or 1T = ~¥,.. Yan Dunjie further suggested that perhaps the value of Yz/0,45 for 1T given by Zhu Zaiyu [at] toward the end of the Ming dynasty could have been derived from Wang Fan's value. This is only a hypothesis. What appears certain, however, is that after the Han period there was considerable interest in a plausible method for approximating 1T based on theoretical foundation. D. 263 succeeded in giving one was Liu Hui. Liu strove for precision and refused "to follow the ancients" (zhong gu Lau]).

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