圆周率π的计算

圆周率π的计算(论文10000字)
摘要：π的值是一个固定不变的数，它在生产生活中起到相当至关重要的作用，对它的产生和发展的过程的研究，至今都经久不衰。在先代人伟业的基础上，进行了考察。对π的钻研提出了本人的认识，并对许多计算π的方法进行了编程比较。主要研究内容如下：
一首先，论述了国内外对π的历史认知。指出在科学发展尚不完善的古代，地理相对位置也不尽相同，π值的计算结果大多也不准确，但它被不约而同地认为是一个常数。
二讨论了π计算的发展历史。单单几何算法的方面来讲，希腊古代最早提出科学计算π值的办法的是阿基米德。得到π的近似值。无独有偶，在我国古时候，第一个精确计算π值的是刘徽，他创造了割圆术，以此取得了π在理论上行之有效的计算方法。然而就分析算法来讲，梅钦公式则称得上是用来计算π值最为行之有效的办法了。如果谈论在其他学科上的进步的话，那么BiFeng投针法就不得不提。
三首先，针对刘徽割圆进行了操作流程的概要论述，并进一步剖析这其中包含的极限思想、思路、创造性思维和科学思想。最后，本人针对祖冲之所做出的约率、密率的产生原因分析，就研究结果表明约率应该是祖冲之在修订徽率过程中所形成的结果，而密率的得出应该与调整日法，连分数法，不定方程的方法有着密不可分的关系。

四对其中一些求解圆周率算的方法进行总结并编程实现进行比较。
关键词：圆周率算法；割圆术；化圆为方；无理性超越性；圆周率的计算

Calculations of π
Abstract：The value of π is a fixed and constant number. It stands as quite a role among the life and production, and the research on the process of its production and development has been a long time. On the basis of previous work, this part is inspected. We put forward our own opinions on the research of π, and compared many methods of computing π. The mainly content of my research comes below:
Firstly，it expounds the historical knowledge of π at home and abroad. It stands that even ancient ways of explore are not good enough like now and they lived in different position, π is just a about number, but they all considered it as a fixed number.
Secondly, the history of the process of π is discussed. In terms of geometric algorithm, the earliest method of calculating π value in ancient Greece was Gu Achmed. The about value of π is obtained. However, in ancient China, Liu Hui, a man who fistly accurately calculate the π value, created the circle cuting area measure, and obtained the  method of π in theory. For the analysis algorithm, the Ma Ching formula is the most effective way to calculate the π value. For Bi Feng needle injection, this is the product of further development of other subjects in mathematics. [资料来源：http://think58.com]
Thirdly, First of all, we briefly introduce the process of Liu Hui circle cutting, just after they have the limit conception, creative thinking and scientific thinking of circular cutting technology. Finally, the author sums up the causes of Zu Chongzhi's rate and the density, and finds that the rate is the result of Zu Chongzhi's modification of the Hui rate, and it may be a consequence of adjusting the diurnal method, or fractional method, and the indeterminate equation. Fourthly, Summarize some of the methods for calculating π and compare them with programming.
Key words：circle cutting;  circle oriented;  irrational transcendence;  calculations of π

目 录
摘要：    3
1.引言    5
2.圆周率的发现与认识    5
2.1历史上中国数学家对圆周率的认识    7
2.2国外历史上有关圆周率值的记载    10
3.圆周率的部分计算公式    12
3.1 Machin公式    12

[资料来源：http://www.THINK58.com]

3.2 Ramanujan公式    12
3.3 AGM(Arithmetic-Geometric Mean)算法    13
3.4 Borwein四次迭代式    14
3.5 Bailey-Borwein-Plouffe算法    14
4.圆周率计算的编程实现    14
4.1 Machin公式算法实现    14
4.2割圆术算法实现    15
4.3格雷戈里莱布尼茨无穷级数算法实现    15
4.4蒙特卡罗法    16
5.圆周率计算编程结果的比较分析    16
结束语    17
参考文献：    17
致谢    19
附件    20
  [来源：http://www.think58.com]