Chinese Mathematics - Mathematics in The Period of Disunity

Mathematics in The Period of Disunity

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 integral and the differential 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 used He Chengtian's interpolation method 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 used the Cavalieri Method to find an accurate solution for calculating the volume of the sphere. 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 around 400 CE contained the most detailed step by step description of multiplication and division algorithm with counting rods. The earliest record of multiplication and division algorithm using Hindu Arabic numerals was in writing by Al Khwarizmi in early 9th century. Khwarizmi's step by step division algorithm was completely identical to Sunzi division algorithm described in Sunzi mathematical classic four centuries earlier. Khwarizmi's work was translated in to Latin in the 13th century and spread to the west, the division algorithm later evolved into Galley division. The route of transmission of Chinese place value decimal arithmetic know how to the west is unclear, how Sunzi's division and multiplication algorithm with rod calculus ended up in Hindu Arabic numeral form in Khwarizmi's work is unclear, as al Khwarizmi never given any Sankrit source nor quoted any Sanskrit stanza. However, the influence of rod calculus on Hindu division is evident, for example in the division example, 324 should be 32400, only rod calculus used blanks for zeros.

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.