Editing Chinese mathematics (section)

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{{History of science and technology in China}}
Mathematics emerged independently in China by the 11th century BCE.<ref>[https://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Chinese_overview.html Chinese overview<!-- Bot generated title -->]</ref> The Chinese independently developed a [[real number]] system that includes significantly large and [[negative number]]s, more than one [[numeral system]] ([[base 2|binary]] and [[base 10|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 [[simple continued fraction]]s are widely used and have been well-documented ever since. They deliberately find the principal [[nth root|''n''th root]] of positive numbers and the [[zero of a function|roots of equation]]s.{{sfn|Needham|1959|pp=65–66}}<ref name=":03">{{Britannica |1238455|East Asian mathematics|Karine Chemla}}</ref> 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.{{sfn|Needham|1959}} All procedures were computed using a counting board in both texts, and they included [[inverse element]]s as well as [[Euclidean division]]s. The texts provide procedures similar to that of [[Gaussian elimination]] and [[Horner's method]] for [[linear algebra]].{{sfn|Needham|1955}} 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#History|Pythagorean theorem]] for example, [[Zhoubi Suanjing|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 [[Blaise Pascal|Pascal]],<ref>{{Cite book |last1=Swetz |first1=Frank J. |title=Was Pythagoras Chinese? an examination of right triangle theory in ancient China |last2=Kao |first2=T. I. |date=1988 |publisher=Pennsylvania State University Press |isbn=978-0-271-01238-4 |location=University Park, Pa}}</ref> such as the Song-era polymath [[Shen Kuo]].