History of Mathematics

irfan3 — 2017-01-19 08:11:30 UTC

History of Mathematics: Chinese Civilization (Mariyah and Khushi)

2017-02-24 05:43:16 UTC

The first thing to understand about ancient Chinese mathematics is the way in which it differs from Greek mathematics. Unlike Greek mathematics there is no axiomatic development of mathematics. Chinese mathematics was, like their language, very concise and very much problem based, motivated by problems of the calendar, trade, land measurement, architecture, government records and taxes. By the fourth century BC counting boards were used for calculating, which effectively meant that a decimal place valued number system was in use. It is worth noting that counting boards are uniquely Chinese, and do not appear to have been used by any other civilisation.
The most famous Chinese mathematics book of all time is the Jiuzhang suanshu or, as it is more commonly called, the Nine Chapters on the Mathematical Art.
Liu Hui gave a more mathematical approach than earlier Chinese texts, providing principles on which his calculations are based. He found approximations to π using regular polygons with 3 × 2ⁿsides inscribed in a circle. His best approximation of π was 3.14159 which he achieved from a regular polygon of 3072 sides. It is clear that he understood iterative processes and the notion of a limit.
One of the most significant advances was by Zu Chongzhi (429-501) and his son Zu Geng (about 450 - about 520). Zu Chongzhi was an astronomer who made accurate observations which he used to produce a new calendar, the Tam-ing Calendar (Calendar of Great Brightness), which was based on a cycle of 391 years. He wrote the Zhui shu (Method of Interpolation) in which he proved that 3.1415926 < π < 3.1415927. He recommended using ³⁵⁵/₁₁₃ as a good approximation and ²²/₇ in less accurate work.
Let us mention one important family, however, namely the Mei family. The most famous member of this family was Mei Wending (1633-1721) and his comment on the golden section is typical of the sensible attitude he took towards Western mathematics (see for example [9]):-

After having understood how to make use of the golden section, I began to believe that the different geometrical methods could be understood and that neither the missionaries attitude of considering this simple technique as a divine gift, nor the Chinese attitude of rejecting it as heresy is correct.
It is to the credit of Chinese mathematicians that they did not let their mathematical tradition be replaced by the western tradition. For example Li Shanlan (1811-1882) is important as a translator of Western science texts but he is most famous for his own mathematical contributions. He produced his own versions of logarithms, infinite series, and combinatorics which did not follow the style of western mathematics but his research naturally developed out of the foundations of Chinese mathematics. There were many other efforts to promote Chinese mathematics, and in particular a mathematics journal, the Suanxue bao, was set up in 1899. The editors wrote:-
"Western methods should not be adulated and Chinese methods despised.”
http://www-history.mcs.st-and.ac.uk/HistTopics/Chinese_overview.html
http://www-history.mcs.st-and.ac.uk/HistTopics/Nine_chapters.html

2017-03-01 07:48:05 UTC

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History of Mathematics: Chinese Civilization (Mariyah and Khushi)