Liu Hui

Liu Hui was a Chinese mathematician of the third century whose commentary on The Nine Chapters on the Mathematical Art explained and extended its methods. He also developed geometric procedures for approximating π.

The Nine Chapters on the Mathematical Art: A foundational Chinese mathematical text organized into nine chapters of problems and procedures. Liu Hui’s commentary explains its algorithms and supplies demonstrations for them.
Method of exhaustion: A method of finding areas or volumes by bounding them with increasingly close approximations. Liu Hui’s polygon argument refines bounds toward a circle’s area.
Cao Wei: A Chinese state that ruled northern China from 220 to 266 during the Three Kingdoms period. Liu Hui’s commentary is dated to 263, during Cao Wei rule.
Tang dynasty mathematical canon: The official collection of mathematical texts used in state examinations during the Tang dynasty. Liu Hui’s commentary was incorporated into the transmitted scholarly form of The Nine Chapters.
Chinese mathematics: The mathematical traditions developed in China, including distinctive texts, procedures, and computational tools. Liu Hui worked within a tradition shaped by practical problems and algorithmic methods.
Inscribed polygon: A polygon whose vertices lie on a given circle. He increased the number of polygon sides to make its perimeter approach the circumference.
Three Kingdoms: A period of Chinese history in which Wei, Shu, and Wu competed for control after the Han dynasty. Liu Hui lived during this era of political division.
Zu Chongzhi: A fifth-century Chinese mathematician who obtained highly accurate bounds for π. His celebrated bounds followed Liu Hui’s earlier polygon-based approximation tradition.
Proof: A logical demonstration that establishes a mathematical statement from accepted premises. His commentary often explains why procedures in The Nine Chapters produce correct results.
Archimedes' method of exhaustion: A Greek geometric method that bounds circle measurements using inscribed and circumscribed polygons. It offers a parallel ancient route to approximating π, developed in a different mathematical tradition.

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