圆周率的计算及若干猜想问题初探+文献综述
而作为一个非常重要的常数，人们对于圆周率也产生的许多的猜想，如在 π 的数值式中各数码出现的概率是否相同？π 的小数位排列真的没有一定的规律吗？其中会否出现所有数字排列的组合呢？
本课题首先从圆周率的历史出发，接着介绍一些有代表性的圆周率计算方法，最好结合所有搜索到的相关资料通过概率统计的方法对于以上的猜想做一个初步的验证。
毕业论文关键字：圆周率，历史，计算，猜想，验证
PI calculation and some guess problems
Abstract：
π is a well known figure , from the beginning of recorded history , π aroused the interest of the world. Since when is it considered three times the circumference of a circle is its diameter , this problem has been difficult to research it. Because it is difficult to determine the time . People have been trying to calculate circumference of a circle and then in the end is more than three times the diameter of the question of how much , countless mathematicians immersive , and even escape. From ancient times , only the mathematical constant π has attracted the attention of many mathematicians , so that π also has a level reflecting the mathematical function that era .
As an important constant for many people also have pi guess , such as the probability of the digital values appearing in the formula π is the same ? decimal arrangement π is really not a certain law? Will there be a combination of all numbers which ordered it ?
This paper first departure from the historical ratio of the circumference , and then introduce some representative pi calculation method, combining the best of all search -related information through the methods of probability and statistics for more than conjecture to make a preliminary validation.
Keywords: Pi, History, Calculation, Guess , Validation
目录
1 圆周率的发展四时期 5
1.1 经验性获得时期 5
1.2 几何法推算时期 5
1.3 分析法计算时期 6
1.4 计算机运算时期 7
2 圆周率的计算 8
2.1 圆周率计算的经典公式 8
2.2 连分数法计算 10
2.3 刘徽割圆术 11
2.3 实验法计算 12
3 圆周率的猜想 13
3.1希尔伯特猜想 13
3.2法格逊猜想 13
3.3我的猜想 22
4 论文小结 26
5 参考文献 26
6 致谢 27
1 圆周率的发展四时期
1.1 经验性获得时期
在经验性获得时期的π是没有详细的理论依据的，反而都是从实际的生活中通过经验得到的，所以在这个时期的π值一般精度都不是多高。
在古埃及所留下的两批草纸之一的莱登草纸上有一个例子,“有一块9凯特(即直径为9)的圆形土地,其面积多大，今取其直径的九分之一,即1,则余8,作8乘以8,得64,这个大小就是面积。”。[1]通过上述的例子，我们可以知道，古人通常认为圆的面积大致相当与一个变长等于这个圆直径的 的正方形的面积，我们可以通过公式的计算，可以求得这里的π= ，大约是3.16049。