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Liu Hui
Mathematician of the Cao Wei state whose 263 commentary on the Nine Chapters proved its methods and approximated pi by doubling the sides of an inscribed polygon
In a calculation room, a wide table holds a board of black and yellow counting rods laid in neat bundles, beside an abacus, a ruler and a sheet with a circle divided into equal parts; one person sits at a far desk with their back turned, and terraced fields lie outside.
Also known as Shan Dong Bin Zhou Ren
- Roles
- Mathematician
Almost nothing is recorded of Liu Hui's life; the Treatise on Calendars in the History of Sui says only that he annotated the Nine Chapters in 263, under the last Wei ruler. His commentary on the Nine Chapters on the Mathematical Art (Jiuzhang suanshu) explains the reasoning behind each procedure and often proves it by cutting and rearranging areas. In the chapter on field measurement he inscribed a hexagon in a circle and kept doubling its sides up to a 192-gon, obtaining a value of about 3.14 for pi, later called Hui's ratio. He also wrote a supplementary chapter on double differences for measuring distant heights such as the sun's, which circulated separately from the Tang onward as the Sea Island Mathematical Manual (Haidao suanjing) and was included among the Ten Mathematical Classics. In 1109 the Song court ennobled him posthumously as Baron of Zixiang.
Life and times
Dates Dates unknown; annotated the Nine Chapters in 263