Circle Measurements in Ancient China

  • Lam Lay-Yong
  • Ang Tian-Se


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.


Decimal Place Song Dynasty Mathematical Text Inscribe Circle Page Reference 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Lam Lay-Yong
    • 1
  • Ang Tian-Se
    • 2
  1. 1.Department of MathematicsNational University of SingaporeSingaporeRepublic of Singapore
  2. 2.Department of Chinese StudiesUniversity of MalayaKuala LumpurMalaysia

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