page_title: Chinese mathematics
section_title: Mathematics in the period of disunity
hierarchical_section_title: Chinese mathematics / Mathematics in the period of disunity
caption_attribution_description: English: Damaged Zhu Chung Zih bronze staute. 中文: 被破壞的祖沖之銅像。 Deutsch: Beschädigte Bronzestatue von Zhu Chung Zih
context_page_description: Mathematics in China emerged independently by the 11th century BC. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system, algebra, geometry, number theory and trigonometry.
  In the Han Dynasty, the Chinese made substantial progress on finding the nth root of positive numbers and solving linear congruence equations. The major texts from the period, The Nine Chapters on the Mathematical Art and the Book on Numbers and Computation gave detailed processes to solving various mathematical problems in daily life. 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 and modular method for Diophantine equation, respectively. The achievement of Chinese algebra reached its zenith in the 13th century, when Li Jingzhai invented tiān yuán shù.
context_section_description: 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. He was the first Chinese mathematician to calculate π=3.1416 with his 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.
  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  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"
  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, 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 200–400 CE contained the most detailed step by step description of multiplication and division algorithm with counting rods. Intriguingly, Sunzi may have influenced the development of place-value systems 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 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.
  In the fifth century the manual called "Zhang Qiujian suanjing" discussed linear and quadratic equations. By this point the Chinese had the concept of negative numbers.
caption: Statue of Zu Chongzhi.
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