Trigonometric tables: explicating their construction principles in China.

The trigonometric table and its construction principles were introduced to China as part of calendar reform, spear-headed by Xu Guangqi (1562-1633) in the late 1620s to early 1630s. Chinese scholars attempted and succeeded in uncovering how the construction principles were established in the seventeenth century and then in the eighteenth century expanded to include more algorithms to compute the values of trigonometric lines. Successful as they were in discoursing the construction principles, most Chinese scholars did not actually construct trigonometric tables anew. In the early nineteenth century, a revolutionary approach was developed, which resembles computing a finite sum of power series to trigonometric functions of an arbitrary arc less than a one-half circle. Though hailed by many modern historians as Chinese achievements in developing 'infinite series' of trigonometric functions, this approach was viewed by the actors at the time as a quick means to construct trigonometric tables. Interestingly, even with these 'quick' methods, no trigonometric table was constructed. Besides the fact that constructing a trigonometric table afresh is a time-consuming business, the classification of the trigonometric table and their construction principles into different genres of knowledge by scholars offers an additional explanation of drastically uneven treatment of trigonometric tables and their construction principles. [ABSTRACT FROM AUTHOR]