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Exploring Liu Hui’s Cube Puzzle - References

Author(s): 
Lingguo Bu (Southern Illinois University Carbondale)

References

  1. Banchoff, T. F. (1990). Dimension. In L. A. Steen (Ed.), On the Shoulders of Giants: New Approaches to Numeracy (pp. 11-59). Washington, DC: National Academy Press.
  2. Bolt, B. (1993). A Mathematical Pandora's Box. New York, NY: Cambridge University Press.
  3. Cundy, H. M., & Rollett, A. P. (1961). Mathematical Models (2nd ed.). London, UK: Oxford University Press.
  4. Dauben, J. W. (2007). Chinese Mathematics. In V. Katz (Ed.), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook (pp. 187-384). Princeton, NJ: Princeton University Press.
  5. Guan, S. P., & Ke, Z. M. (2009). Cong Yangma He bie'nao Tan Qi [On Yangma and Bie'nao in Middle Grades Mathematics]. Available at http://www.hkedcity.net/iclub_files/a/1/68/webpage/maths612/YangmaBienao_volume.pdf 
  6. Gardner, M. (2001). The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. New York, NY: W. W. Norton & Company.
  7. Guo, S. C. (2009). Jiu Zhang Suan Shu Yi Zhu [Translation and Annotation of the Nine Chapters on Mathematical Procedures]. Shanghai, China: Shanghai Chinese Classics Press. 
  8. Kriege, M. H. (1876). Friedrich Froebel: A Biographical Sketch. New York, NY: E. Steiger.
  9. Li, W. L. (2002). Shu Xue Shi Gai Lun [A History of Mathematics] (2nd ed.). Beijing, China: Higher Education Press.
  10. Li, Y., & Du, S. R. (1987). Chinese Mathematics: A Concise History (J. N. Crossley & A. W. C. Lun, Trans.). Oxford, UK: Oxford University Press.
  11. Li, H. (1820). Jiu Zhang Suan Shu Xi Cao Tu Shuo [Detailed Commentary on the Nine Chapters on the Mathematical Art with Diagrams]. Available at http://ctext.org/library.pl?if=en&res=3022&by_author=%E6%9D%8E%E6%BD%A2&remap=gb  
  12. Liu, H., & Li, C. (n. d.). Jiu Zhang Suan Shu Zhu Shi [Commentaries on the Nine Chapters on Mathematical Art]. Dai Zhen (Ed.). Qin Ding Si Ku Quan Shu: Zi Bu [Emperor's Complete Library of the Four Branches of Literature: Masters' Branch]. Available at https://archive.org/details/06057482.cn  and http://ctext.org/library.pl?if=en&res=5782&remap=gb 
  13. Martzloff, J.-C. (1987/1997). A History of Chinese Mathematics (S. S. Wilson, Trans.). New York, NY: Springer.
  14. Perkins, D. N. (1986). Knowledge as Design. Hillsdale, NJ: Lawrence Erlbaum Associates.
  15. Shen, K. S., Crossley, J. N., & Lun, A. W. C. (1999). The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford, UK: Oxford University Press.
  16. Silverman, J. (2013). Ancient Chinese Geometry. Available at http://www.jensilvermath.com/2016/06/04/ancient-chinese-geometry-2/ 
  17. Steinhaus, H. (1969). Mathematical Snapshots (3rd ed.). New York, NY: Oxford University Press.
  18. Stewart, I. (2009). Professor Stewart's Cabinet of Mathematical Curiosities. New York, NY: Basic Books.
  19. Weisstein, E. W. (n.d.). Cube. From MathWorld - A Wolfram web resource at http://mathworld.wolfram.com/Cube.html
  20. Wagner, D. B. (1979). An Early Chinese Derivation of the Volume of a Pyramid: Liu Hui, Third Century A.D. Historia Mathematica6, 164-188.
  21. Ying, J. M. (2011). The Kujang sulhae 九章術解: Nam Pyǒng-Gil's reinterpretation of the mathematical methods of the Jiuzhang suanshu. Historia Mathematica38, 1-27.
  22. 四角錐を切り分けてわかる3で割る3つの理由 (n.d.). Retrieved June 23, 2016 from www3.synapse.ne.jp/kintaro/content226.htm.

Also in Convergence

The article "Leonardo Da Vinci's Geometric Sketches" includes images of the tetrahedron and cube, along with the other Platonic solids, created for Luca Pacioli's De divina proportione (1509).

Lingguo Bu (Southern Illinois University Carbondale), "Exploring Liu Hui’s Cube Puzzle - References," Convergence (February 2017)