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A Classic from China: The Nine Chapters

Randy K. Schwartz (Schoolcraft College)


This article is about the most important mathematical work in China’s long history, the Jiuzhang Suanshu (“Nine Chapters on the Art of Calculation”). The book, known today in the West as the Nine Chapters, was used throughout China for centuries, and it also circulated in Korea and Japan, influencing mathematics there. The author(s) and date(s) of the original work are no longer known, but clues in the text indicate that it was probably written shortly after 200 BCE. The mathematician whose name is most closely associated with the Nine Chapters is Liu Hui, who in 263 CE wrote a commentary on the book that included methods and rules from the original, along with justifications for the techniques used. This article will survey the Nine Chapters, illustrating each chapter with a problem or two that is accessible to most high school and college students, and touching on what the the book tells us about Chinese culture of its time.

Editor's note: This article originally appeared in The Right Angle, a newsletter for mathematics students and faculty at Schoolcraft College (Livonia, Michigan), in October of 2008 and is reprinted here (with minor modifications) with the permission of the author and editor of The Right Angle, Randy Schwartz.

Randy K. Schwartz (Schoolcraft College), "A Classic from China: The Nine Chapters," Convergence (December 2018), DOI:10.4169/convergence20181231