The Nine Chapters on the Mathematical Art

An ancient Chinese mathematical text that organized practical methods for arithmetic, geometry, surveying, engineering, and taxation into nine chapters. Its problems and procedures shaped mathematical practice in China for centuries.

Counting rods: Small rods arranged in place-value patterns to represent numbers and perform calculations. The text’s algorithms rely on positional calculation with rods, including operations on counting boards.
Gaussian elimination: An algorithm that solves systems of linear equations by row operations. The fangcheng procedure transforms arrays of coefficients to determine several unknowns.
Han dynasty: A Chinese imperial dynasty that ruled from 206 BCE to 220 CE. The text took shape in the mathematical culture associated with the Han period.
Land surveying: The measurement and mapping of land boundaries, areas, and elevations. Several problems calculate fields and distances for taxation and land administration.
Ten Computational Canons: A collection of ten Chinese mathematical texts designated as classics in the Tang dynasty. The Nine Chapters was the leading work in this canon of mathematical study.
Chinese numerals: Writing systems used to represent numbers in Chinese, including characters and rod-based numerals. Numeral notation provides the language for stating quantities and recording the text’s answers.
Square root algorithm: A digit-by-digit procedure for finding the square root of a number. The text gives a systematic extraction method using place-value calculations.
Liu Hui: A third-century Chinese mathematician who wrote a detailed commentary on The Nine Chapters. His commentary explains procedures and supplies geometric proofs absent from the main text.
Taxation: The levying of compulsory payments by a governing authority. Agricultural area calculations helped assess taxable land and distribute obligations.
Tang dynasty: A Chinese imperial dynasty that ruled from 618 to 907 CE. Tang institutions incorporated the text into formal mathematical education and examinations.

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