Chinese mathematics

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Mathematics emerged independently in China by the 11th century BCE.^[1] The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system (binary and decimal), algebra, geometry, number theory and trigonometry.

Since the Han dynasty, as diophantine approximation being a prominent numerical method, the Chinese made substantial progress on polynomial evaluation. Algorithms like regula falsi and expressions like continued fractions are widely used and have been well-documented ever since. They deliberately find the principal nth root of positive numbers and the roots of equations.^[2][3] The major texts from the period, The Nine Chapters on the Mathematical Art and the Book on Numbers and Computation gave detailed processes for solving various mathematical problems in daily life.^[4] All procedures were computed using a counting board in both texts, and they included inverse elements as well as Euclidean divisions. The texts provide procedures similar to that of Gaussian elimination and Horner's method for linear algebra.^[5] The achievement of Chinese algebra reached a zenith in the 13th century during the Yuan dynasty with the development of tian yuan shu.

As a result of obvious linguistic and geographic barriers, as well as content, Chinese mathematics and the mathematics of the ancient Mediterranean world are presumed to have developed more or less independently up to the time when The Nine Chapters on the Mathematical Art reached its final form, while the Book on Numbers and Computation and Huainanzi are roughly contemporary with classical Greek mathematics. Some exchange of ideas across Asia through known cultural exchanges from at least Roman times is likely. Frequently, elements of the mathematics of early societies correspond to rudimentary results found later in branches of modern mathematics such as geometry or number theory. The Pythagorean theorem for example, has been attested to the time of the Duke of Zhou. Knowledge of Pascal's triangle has also been shown to have existed in China centuries before Pascal,^[6] such as the Song-era polymath Shen Kuo.