Abstract
This paper discusses the method of Liu Hui (3rd century) for evaluating the ratio of the circumference of a circle to its diameter, now known as π. A translation of Liu’s method is given in the Appendix. Also examined are the values for π given by Zu Chongzhi (429–500) and unsurpassed for a millenium. Although the method used by Zu is not extant, it is almost certain that he applied Liu’s method. With the help of an electronic computer, a table of computations adhering to Liu’s method is given to show the derivation of Zu’s results. The paper concludes with a survey of circle measurements in China.
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Lay-Yong, L., Tian-Se, A. (2004). Circle Measurements in Ancient China. In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4217-6_5
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DOI: https://doi.org/10.1007/978-1-4757-4217-6_5
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