An outstanding work that has survived the ravages of time is the Jiuzhang suanshu (Nine chapters on the mathematical art). Dating possibly from 200 BC, it contains the calculation of areas and volumes, the evaluation of square and cube roots, and the systematic solution of simultaneous equations (now called Gaussian elimination).
Several Chinese mathematicians devoted their attention to evaluating pi. Zhang Heng (AD 78–139), inventor of the seismograph for measuring earthquake intensity, proposed the value sqrt10 (about 3.16). Around the year 264 Liu Hui, while revising the Jiuzhang suanshu, calculated the area of a regular polygon with 192 sides and deduced that lies between 3.1410 and 3.1427. This Chinese fascination with pi reached its climax in the 5th century, when Zu Chongzhi and his son calculated the area of a regular polygon with 24,576 sides and deduced that it lies between 3.1415926 and 3.1415927. They also found the estimate of 355/113, which gives pi to six decimal places; this approximation was not rediscovered in the west until the 16th century.
A remarkable work of 1303, the Siyuan yujian (Jade Mirror of Four Elements) shows an early version of the arithmetical triangle of binomial coefficients. This triangle was later analysed by Blaise Pascal and is now named after him.
[China 1955, 2002; Liberia 1999; Micronesia 1999]
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