高师理科学刊2025，Vol.45Issue(10)：1-4,4.DOI:10.3969/j.issn.1007-9831.2025.10.001
利用割圆术计算圆周率的一个改进迭代公式
An improved iterative formula for calculating π by using the method of inscribed polygons
摘要
Abstract
The method of inscribed polygons was the primary method for calculating π in ancient times,where only the four basic arithmetic operations as well as the extraction of square roots could be used.Manual computation of square roots is inherently challenging,and even more so for ancient mathematicians.Consequently,reducing the number of square root operations hold critical significance for enhancing both the accuracy and efficiency.The paper briefly revisits LIU Hui's method of inscribed polygons at first,and then presents a new iterative formula for calculating the side length of the inscribed polygons.The new formula reduces the number of square root operations,and thus it is easier to calculate the value of π by using the method of inscribed polygons.关键词
割圆术/圆周率/迭代Key words
method of inscribed polygons/π/iteration分类
数学引用本文复制引用
王在华,李静..利用割圆术计算圆周率的一个改进迭代公式[J].高师理科学刊,2025,45(10):1-4,4.基金项目
陆军工程大学教育教学课题(GJ23ZD009) （GJ23ZD009）
