The Cutting Circle Method and Romberg Algorithm

Using the cutting circle method to calculate the value of π was firstly proposed by the Chinese mathematician Liu Hui in Three Kingdoms Era, around the third century AD. Two hundred years later, the Northern and Southern mathematician Zu got a comparative accurate approximation of π by using this method. This paper analyzed Liu Hui's cutting circle method and pointed out that it is essentially a combination of the cutting circle method and an acceleration technology. And this method can deal with several rough initial data to achieve a good acceleration effect after appropriately adjust the combination coefficients. Finally, the Romberg algorithm is used to combine with Liu Hui's cutting circle method to calculate the value of π, and find that only four initial data can be calculated to obtain a relatively accurate approximation of π.