割圆术

印度的割圆术与π值

Indian cyclotomic method and the value of π

用VISUALBASIC编程演示割圆术的实现过程

Demonstrating Realizing Process of " Cyclotomic Technique " by Visual Basic

基于割圆术计算π的一种快速逼近算法

Quick approach algorithm of π calculation based on cutting circle method

割圆术与穷竭法

The method of cutting circle and infinite approach

一组新的割圆术不等式

New Inequalities for Circle - Cutting Technique

晚清算家倾向于摆脱割圆术的逻辑基础而非直观基础。

Late Qing mathematicians tried to be free from logic but not from empiric of the cyclotomy .

后继者祖冲之利用割圆术得出了正确的小数点后七位。

the student surpasses the teacher . Lat-er , with Liu 's method ， Zu Chongzhi determined pi to 7 digits .

“割圆术”包含近代极限思想，其过程是一个无限过程，可以创造崭新结果；

But the method of infinite approach is used more widely , it is a uninfinite procedure , and it only can achieve the desired results with reduction to absurdity .

在求准确圆周率值的征途中，首先迈出关键一步的是三国时期魏国杰出的数学家刘徽。他创立割圆术，用圆内接正多边形无限逼近圆而求取圆周率值。

On the journey of finding a precise pi ， Liu Hui ， a prominent mathematician of the Kingdom of Wei during the Three Kingdoms period ， took the first crucial step by approximated pi .

本文是文[1]的续篇，进一步阐述割圆术的思维模式对现代演化数学研究的启迪意义。

This is sequel of the paper [ 1 ] , which makes a further exposition on the thinking model of " Cutting Circle Method " and its significant enlightenment on studying modern evolutionary mathematics .

对基于割圆术计算π的算法进行研究，介绍一种计算π的快速逼近算法，由泰勒公式只用很少的多边形就可得到具有高精度的计算结果。

Research into algorithm of π calculation based on cutting a circle method in this paper . Quick approach algorithm of π calculation is introduced . By Taylor formula , a few polygons are used and calculating result with high precision is obtained .