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.