论文部分内容阅读
一、刘徽割圆术在华罗庚教授所写的“从祖冲之的圓周率談起”一书中指出:在一千多年以前祖冲之就已經知道: (ⅰ) 圆周率π,在3.1415926与3.1415927之間; (ⅱ) 以22/7作为π的約率,以355/113作为密率。他还提到:“这些結果是刘徽割圓术之后的重要发展。刘徽从圓内接正六边形起算,令边数一倍一倍地增加,即12,24,48,96,……,1536,……,因而逐个算出六边形,十二边形,二十四边形,……的面积,这些数值逐步逼近圓周率。刘徽方法的特点,是得出一批一个大于一个的数值,这样来一步一步地逼近圓周率。这方法是可以无限精密地逼近圓周率的。但每一次都比圆
First, Liu Hui’s circumcision was written by Professor Hua Luogeng in the book “Talking from the Circumference Rate of Zu Chongzhi”: Zu Chongzhi already knew about a thousand years ago: (i) pi, between 3.1415926 and 3.1415927; (ii) Take 22/7 as the ratio of π and 355/113 as the density. He also mentioned: "These results are important developments after Liu Hui’s cutting operation. Liu Hui counts from the hexagon in the circle and increases the number of edges by a factor of two, that is, 12,24,48,96,... ...,1536,..., So calculate the areas of hexagons, dodecagons, octagons, ..., and these values are gradually approaching the pi. The characteristics of Liu Hui’s method is to draw a group of more than one. The value of this is to approach the pi in step by step. This method can approximate the pi in infinite precision, but every time it is more than a circle.