References for: Nine Chapters on the Mathematical Art


Version for printing
Books:
  1. V I Ilyushchenko, Gauss elimination method (1849 AD) in the ancient Chinese script Mathematics in nine chapters (152 BC), Communications of the Joint Institute for Nuclear Research (Dubna, 1992).
  2. J-C Martzloff, A history of Chinese mathematics (Berlin-Heidelberg, 1997).
  3. J-C Martzloff, Histoire des mathématiques chinoises (Paris, 1987).
  4. K Shen, J N Crossley and A W-C Lun, The nine chapters on the mathematical art : Companion and commentary (Beijing, 1999).
Papers:
  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. C Cullen, Learning from Liu Hui? A different way to do mathematics, Notices Amer. Math. Soc. 49 (7) (2002), 783-790.
  6. J W Dauben, The "Pythagorean theorem" and Chinese mathematics : Liu Hui's commentary on the gou-gu theorem in Chapter Nine of the J'iu zhang suan shu', in Amphora (Basel, 1992), 133-155.
  7. Z Q Deng, A comparative study of the Jiu zhang suanshu and the Elements (Chinese), J. Central China Normal Univ. Natur. Sci. 28 (2) (1994), 263-268.
  8. 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.
  9. D W Fu, Why did Liu Hui fail to derive the volume of a sphere?, Historia Math. 18 (3) (1991), 212-238.
  10. 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.
  11. S C Guo, Guo Shuchun's edition of the 'Jiuzhang Suanshu' ('Nine chapters on the mathematical art'), Historia Math. (2) 19 (1992), 200-202.
  12. W S Horng, How did Liu Hui perceive the concept of infinity : a revisit, Historia Sci. (2) 4 (3) (1995), 207-222.
  13. B S Hu, A further study on the positive-negative principle in the Jiu zhang suanshu (Chinese) , in Collected research papers on the history of mathematics Vol. 2 (Hohhot, 1991), 31-34.
  14. L Y Lam, 'Jiu zhang suanshu' ('Nine chapters on the mathematical art') : an overview, Arch. Hist. Exact Sci. 47 (1) (1994), 1-51.
  15. J M Li, A textual criticism on the "art of milü" in ring measurement in Nine chapters on arithmetic (Chinese), J. Northwest Univ. 21 (2) (1991), 1-6.
  16. Z J Liang, From the elimination method in the Jiu zhang suanshu (Arithmetic in nine sections) to automated theorem proving (Chinese), J. Central China Normal Univ. Natur. Sci. 33 (2) (1999), 179-185.
  17. 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.
  18. 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.
  19. 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.
  20. Z C Shang, A comparison of the Elements and Wei Liu's notes on the theory of proportion and its applications in Jiu Zhang Suanshu (Chinese), in Studies on Euclid's Elements (Hohhot, 1992) , 217-233.
  21. 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.
  22. J Song, The historical value of the 'Nine chapters on the mathematical art' in society and the economy, in Chinese studies in the history and philosophy of science and technology 179 (Dordrecht,1996), 261-266.
  23. P D Straffin Jr, Liu Hui and the first golden age of Chinese mathematics, Math. Mag. 71 (3) (1998), 163-181.
  24. D B Wagner, A proof of the Pythagorean theorem by Liu Hui (third century AD), Historia Math. 12 (1) (1985), 71-73.
  25. 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.
  26. R B Wang, A preliminary exploration on the logical order of the Shang gong chapter of Jiu zhang suanshu - a parallel discussion on the understanding of the operational rule ab+ac=a(b+c) in 'Jiu zhang' (Chinese), in Collected research papers on the history of mathematics Vol. 2 (Hohhot, 1991), 35-39.
  27. 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.
  28. 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.

JOC/EFR December 2003

The URL of this page is:
http://www-history.mcs.st-andrews.ac.uk/HistTopics/References/Nine_chapters.html