Exploring Liu Hui’s Cube Puzzle - Appendix: Chinese Text for Liu Hui's Cube Dissection

Liu Hui’s Commentary in Chinese on Problem Fifteen of Chapter Five in the Nine Chapters on the Mathematical Art

Jiu Zhang Suan Shu (Nine Chapters on the Mathematical Art) is an ancient Chinese mathematical text which was probably complied and annotated over time by many mathematicians. Liu Hui’s commentaries around 263 AD comprise the best known version and are widely considered the foundation of traditional Chinese mathematics. These commentaries were further annotated by successive mathematicians in the ensuing centuries (Lui & Li, n.d.; Sheng, Crossley & Lun, 1999). Thus, there exist various versions of the famous mathematical text even in the Chinese language. The following excerpts are screenshots of Liu Hui’s Chinese comments on Problem 15 of Chapter 5 from an official version of the Nine Chapters, appearing in the Masters’ Branch of Si Ku Quan Shu (Emperor’s Complete Library of the Four Branches of Literature) available at https://archive.org/details/06057482.cn. As is typical of ancient Chinese text, it should be read from the top to the bottom and from the right to the left.

Figure 21a. Part I of Liu Hui’s comment on Problem 15 of Chapter 5 about the volume of a yangma (rectangular pyramid). Screenshot from https://archive.org/details/06057482.cn

Figure 21b. Part II of Liu Hui’s comment on Problem 15 of Chapter 5 about the volume of a yangma (rectangular pyramid). Screenshot from https://archive.org/details/06057482.cn