263 CE / East Asia
Liu Hui explains why the Nine Chapters' procedures work
Liu Hui comments on inherited mathematical procedures, connecting calculation with geometric reasoning, including a method for approximating circles.
The story
The Nine Chapters accumulated material over generations; 263 dates Liu Hui's commentary, not the book's original creation. He examined why methods for areas, volumes and equations worked, and developed circle-cutting arguments. Commentary could thus create new mathematics rather than merely preserve answers.
Connections and context
Euclid and Liu Hui organize reasoning differently. Their traditions should not be reduced to a hierarchy of proof versus mere calculation.
Dates and precision
263 CE Documented date
Positioned by the documented year, month or day. Missing precision is not inferred.
Representative map location
Linzi region (traditional biographical association)
A regional biographical reference; evidence for his life and the commentary's place of composition is limited.
Representative coordinates · 36.82°, 118.31°
A marker identifies one representative place, such as a manuscript collection, laboratory or observing site. It does not mean the work happened only there, or assign a shared discovery to one country.
Bibliography
- Chinese Academy of Sciences, IHNS | Liu Hui and the Nine Chapters commentary
- 中国科学院自然科学史研究所｜《自然科学史研究》2000年第2期：有关《九章算术》的一些讨论
References are listed as plain bibliography titles. They support particular facts or context; a reference does not certify every interpretation in a story.