Editing Chinese mathematics (section)

==Three Kingdoms, Jin, and Sixteen Kingdoms==
[[File:Sea_island_survey.jpg|right|thumb|148x148px|Liu Hui's Survey of sea island]]
[[File:Sunzi_division.GIF|left|thumb|100x100px|Sunzi algorithm for division 400 AD]]
[[File:AL_Khwarizmi_division.GIF|right|thumb|100x100px|al Khwarizmi division in the 9th century]]
[[File:Juchungzi.jpg|left|thumb|287x287px|Statue of [[Zu Chongzhi]].]]
In the third century [[Liu Hui]] wrote his commentary on the Nine Chapters and also wrote [[Haidao Suanjing]] which dealt with using Pythagorean theorem (already known by the 9 chapters), and triple, quadruple triangulation for surveying; his accomplishment in the mathematical surveying exceeded those accomplished in the west by a millennium.<ref>{{Cite book |last1=Swetz |first1=Frank J. |url=https://archive.org/details/isbn_2083776009956 |title=The sea island mathematical manual: surveying and mathematics in ancient China |last2=Liu |first2=Hui |date=1992 |publisher=Pennsylvania State University Press |isbn=978-0-271-00795-3 |location=University Park, Pa |pages=63 |access-date=2023-11-18}}</ref> He was the first Chinese mathematician to calculate ''π''=3.1416 with his [[Liu Hui's π algorithm|''π'' algorithm]]. He discovered the usage of [[Cavalieri's principle]] to find an accurate formula for the volume of a cylinder, and also developed elements of the [[infinitesimal calculus]] during the 3rd century CE.
[[File:Diaorifa.GIF|right|thumb|90x90px|fraction interpolation for pi]]
In the fourth century, another influential mathematician named [[Zu Chongzhi]], introduced the ''Da Ming Li.'' This calendar was specifically calculated to predict many cosmological cycles that will occur in a period of time. Very little is really known about his life. Today, the only sources are found in [[Book of Sui]], we now know that Zu Chongzhi was one of the generations of mathematicians. He used Liu Hui's pi-algorithm applied to a 12288-gon and obtained a value of pi to 7 accurate decimal places (between 3.1415926 and 3.1415927), which would remain the most accurate approximation of π available for the next 900 years. He also applied He Chengtian's interpolation for approximating irrational number with fraction in his astronomy and mathematical works, he obtained <math>\tfrac{355}{113}</math> as a good fraction approximate for pi; Yoshio Mikami commented that neither the Greeks, nor the Hindus nor Arabs knew about this fraction approximation to pi, not until the Dutch mathematician Adrian Anthoniszoom rediscovered it in 1585, "the Chinese had therefore been possessed of this the most extraordinary of all fractional values over a whole millennium earlier than Europe".{{sfn|Mikami|1913|p=50}}

Along with his son, Zu Geng, Zu Chongzhi applied the Cavalieri's principle to find an accurate solution for calculating the volume of the sphere. Besides containing formulas for the volume of the sphere, his book also included formulas of cubic equations and the accurate value of pi. His work, ''Zhui Shu'' was discarded out of the syllabus of mathematics during the Song dynasty and lost. Many believed that ''Zhui Shu'' contains the formulas and methods for [[Linear algebra|linear]], [[Matrix (mathematics)|matrix algebra]], algorithm for calculating the value of ''π'', formula for the volume of the sphere. The text should also associate with his astronomical methods of interpolation, which would contain knowledge, similar to our modern mathematics.

A mathematical manual called ''Sunzi mathematical classic'' dated between 200 and 400&nbsp;CE contained the most detailed step by step description of [[Rod calculus#Multiplication|multiplication]] and division algorithm with counting rods. Intriguingly, ''Sunzi'' may have influenced the development of [[place-value system]]s and place-value systems and the associated [[Galley division]] in the West. European sources learned place-value techniques in the 13th century, from a Latin translation an early-9th-century work by [[Al-Khwarizmi]]. Khwarizmi's presentation is almost identical to the [[Rod calculus#Division|division algorithm in ''Sunzi'']], even regarding stylistic matters (for example, using blank spaces to represent trailing zeros); the similarity suggests that the results may not have been an independent discovery. Islamic commentators on Al-Khwarizmi's work believed that it primarily summarized Hindu knowledge; Al-Khwarizmi's failure to cite his sources makes it difficult to determine whether those sources had in turn learned the procedure from China.<ref name="LayYongArithmeticSystems2">{{Cite journal |last=Lam Lay Yong |year=1996 |title=The Development of Hindu Arabic and Traditional Chinese Arithmetic |url=https://sciences.aum.edu/~sbrown/Hindu%20Arabic%20and%20Chinese.pdf |url-status=dead |journal=Chinese Science |volume=13 |pages=35–54 |archive-url=https://web.archive.org/web/20120321111930/https://sciences.aum.edu/~sbrown/Hindu%20Arabic%20and%20Chinese.pdf |archive-date=2012-03-21 |access-date=2015-12-31}}</ref>

In the fifth century the manual called "[[Zhang Qiujian Suanjing|Zhang Qiujian suanjing]]" discussed linear and quadratic equations. By this point the Chinese had the concept of [[negative numbers]].