Approximation Formulae in Chinese Mathematics
Approximation formulae may be used for various reasons. In some cases, certain computations (such as for example, the extraction of roots digit by digit) are by nature inexact. It may also be that exact solutions of certain problems are unknown or else that such solutions are theoretically known but deemed too complex, so that users prefer elaborating alternative solutions more or less accurate with respect to a certain context of utilization. The history of Chinese mathematics illustrates well these two aspects of the question.
Remarkably, many Chinese approximation formulae are also attested in Babylonian, Greek, Roman, Indian, and Mediaeval European mathematics. For example, the so‐called “Hero's iteration formula” for the approximation of square roots converges quadratically to x is also found in the Jiuzhang suanshu (Computational Prescriptions in Nine Chapters, also translated as Nine Chapters on the Mathematical Arts) from the Han dynasty (206 BCE–AD 220).
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