Yang Hui

Yang Hui was a Chinese mathematician of the Southern Song dynasty whose writings discussed arithmetic, magic squares, and a triangular arrangement of binomial coefficients.

Pascal's triangle: A triangular arrangement of binomial coefficients in which each interior entry is the sum of the two above it. Yang Hui described this arrangement centuries before it became widely known in Europe by Pascal's name.
Southern Song dynasty: The Chinese dynasty that ruled southern China from 1127 to 1279 after the loss of the northern capital. Yang Hui lived and wrote during this period of political division and commercial growth.
Chinese remainder theorem: A theorem giving conditions for solving systems of congruences with different moduli. It exemplifies the modular arithmetic problems treated in the Chinese mathematical tradition Yang Hui inherited.
Zhu Shijie: A Chinese mathematician of the Yuan dynasty known for algebraic works including Jade Mirror of the Four Unknowns. His later scholarship shows the continued development of Chinese mathematics after Yang Hui's lifetime.
Binomial coefficient: An integer counting ways to choose a fixed number of objects from a larger set; it also appears in binomial expansions. Its coefficients form the triangular arrangement associated with Yang Hui.
Qin Jiushao: A thirteenth-century Chinese mathematician known for his 1247 treatise, Mathematical Treatise in Nine Sections. His work provides a near-contemporary comparison for Song mathematical scholarship.
False position method: An arithmetic procedure for solving a problem by adjusting an estimated value in proportion to its error. Yang Hui's mathematical writings preserve the procedural style used to solve numerical problems.
Jia Xian triangle: An early Chinese triangular arrangement of binomial coefficients associated with the mathematician Jia Xian. This name emphasizes the earlier source Yang Hui credited for the arrangement.
Magic square: A square grid of numbers whose rows, columns, and main diagonals share the same sum. Yang Hui's writings include methods and examples involving these number grids.
Jia Xian: An eleventh-century Chinese mathematician associated with an early method for generating binomial coefficients. Yang Hui attributed the triangular coefficient arrangement to an earlier mathematical tradition associated with Jia Xian.

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