源于割圆术的Pi值算法设计与Python实现

Design and Python Implementation of Pi Value Algorithms Derived from Circle Cutting

本文设计了一种计算圆周率Pi的算法,并编制了Python程序加以实现和验证。此算法源于中国古代刘徽首创的割圆术。通过迭代计算的逐步推导,从周长和面积两个角度具体阐述算法的内容,并依据误差估计从理论层面证明算法的正确性。之后给出简要的算法描述,并据此完成代码编写。依次在不同的Pi精度要求下运行通过,从实践层面实现算法并验证其正确性;实际测算了程序的运行耗时和误差表现,直观反映出算法的计算效率和计算精度。

This paper designs an algorithm for calculating Pi,and compiles a Python program to implement and verify it.This algorithm originated from the circle cutting technique initiated by Liu Hui in ancient China.Through the gradual derivation of iteration calculation,the content of the algorithm is elaborated from the perimeter and area,and the correctness of the algorithm is proved from the theoretical level based on error estimation.Then a brief description of the algorithm is given,and the code is written accordingly.It runs under different Pi precision requirements,realizes the algorithm from the practical level and verifies its correctness.It calculates the running time and error performance of the program,which directly reflects the calculation efficiency and accuracy of the algorithm.