References for Liu Hui


  1. H Peng-Yoke, Biography in Dictionary of Scientific Biography (New York 1970-1990).
    http://www.encyclopedia.com/doc/1G2-2830902643.html

Books:

  1. J-C Martzloff, A history of Chinese mathematics (Berlin-Heidelberg, 1997).
  2. J-C Martzloff, Histoire des mathématiques chinoises (Paris, 1987).
  3. K Shen, J N Crossley and A W-C Lun, The nine chapters on the mathematical art : Companion and commentary (Beijing, 1999).

Articles:

  1. T S Ang and F J Swetz, A Chinese mathematical classic of the third century : the 'Sea island mathematical manual' of Liu Hui, Historia Math. 13 (2) (1986), 99-117.
  2. S S Bai, A re-examination of a ring area problem in the 'Jiu zhang suanshu' (Chinese), Beijing Shifan Daxue Xuebao 30 (1) (1994), 139-142.
  3. E I Berezkina (trs.), Two texts of Liu Hui on geometry (Russian), in Studies in the history of mathematics, No. 19 (Russian) (Moscow, 1974), 231-273.
  4. K Chemla, Different concepts of equations in 'The nine chapters on mathematical procedures' and in the commentary on it by Liu Hui (3rd century), Historia Sci. (2) 4 (2) (1994), 113-137.
  5. K Chemla, Relations between procedure and demonstration : Measuring the circle in the 'Nine chapters on mathematical procedures' and their commentary by Liu Hui (3rd century), in History of mathematics and education: ideas and experiences (Essen, 1992) (1996), 69-112.
  6. C Cullen, Learning from Liu Hui? A different way to do mathematics, Notices Amer. Math. Soc. 49 (7) (2002), 783-790.
    http://www.ams.org/notices/200207/comm-cullen.pdf
  7. J W Dauben, The 'Pythagorean theorem' and Chinese mathematics : Liu Hui's commentary on the gou-gu theorem in Chapter Nine of the 'Jiu zhang suan shu', in Amphora (Basel, 1992), 133-155.
  8. Y Z Dong and Y Yao, The mathematical thought of Liu Hui (Chinese), Qufu Shifan Daxue Xuebao Ziran Kexue Ban 13 (4) (1987), 99-108.
  9. L S Feng, 'Jiu zhang suanshu' and Hui Liu's theory of similar right triangles (Chinese), in Collected research papers on the history of mathematics, Vol. 1 (Chinese) (Hohhot, 1990), 37-45.
  10. D W Fu, Why did Liu Hui fail to derive the volume of a sphere?, Historia Math. 18 (3) (1991), 212-238.
  11. S C Guo, Liu Hui's great contributions to mathematics : celebrating the 1720th anniversary of his commentary on the 'Jiu zhang suanshu' (Chinese), Math. Practice Theory (3) (1983), 75-79.
  12. X H Guo, On Liu Hui's 'qiyan method' (Chinese), J. Central China Normal Univ. Natur. Sci. 20 (3) (1986), 400-408.
  13. W S Horng, How did Liu Hui perceive the concept of infinity : a revisit, Historia Sci. (2) 4 (3) (1995), 207-222.
  14. D Liu, A comparison of Archimedes' and Liu Hui's studies of circles, in Chinese studies in the history and philosophy of science and technology 179 (Dordrecht, 1996), 279-287.
  15. R Mei, Liu Hui's theories of mathematics, in Chinese studies in the history and philosophy of science and technology 179 (Dordrecht, 1996), 243-254.
  16. S K Mo, 'Jiuzhang suanshu' ('Nine chapters on the mathematical art') and Liu Hui's commentary (Chinese), Stud. Hist. Nat. Sci. 19 (2) (2000), 97-113.
  17. H H Shou, L G Liu and G J Wang, An offset approximation algorithm based on Liu Hui's circle subdivision method (Chinese), Appl. Math. J. Chinese Univ. Ser. A 17 (1) (2002), 105-112.
  18. P D Straffin Jr, Liu Hui and the first golden age of Chinese mathematics, Math. Mag. 71 (3) (1998), 163-181.
  19. A Volkov, Calculation of pi in ancient China : from Liu Hui to Zu Chongzhi, Historia Sci. (2) 4 (2) (1994), 139-157.
  20. D B Wagner, A proof of the Pythagorean theorem by Liu Hui (third century AD), Historia Math. 12 (1) (1985), 71-73.
  21. D B Wagner, An early Chinese derivation of the volume of a pyramid : Liu Hui, third century AD, Historia Math. 6 (2) (1979), 164-188.
  22. X Q Wang, Elementary studies on pi in France in the 17th - 19th centuries and Liu Hui's cyclotomic rule (Chinese), J. Zhejiang Univ. Sci. Ed. 30 (1) (2003), 1-6.
  23. Z W Xi and S L Zhang, On the characteristic of the dialectical thought of the 'Jiu zhang suanshu' and Hui Liu's commentary (Chinese), Qufu Shifan Daxue Xuebao Ziran Kexue Ban 19 (4) (1993), 103-110.
  24. S C Yang, 'Ratio' and 'power' in Hui Liu's commentary on the 'Jiu zhang suan shu' ('Arithmetic in nine chapters') (Chinese), Dongbei Shida Xuebao (4) (1990), 39-43.

December 2003


MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/References/Liu_Hui.html]