无理数

First, when the Pythagoreans discovered the irrationality of the square root of two … Second, when the philosophical Bishop, Berkeley the Bear, pointed out the contradiction of dividing by zero … But Cantor the Goat, by his General Set Theory, has shown us how to resolve these problems, and to dispel crisis from the Foundations of Mathematics!

每一次危机是毕达哥拉斯学派发现了2的平方根是一个无理数……第二次危机是作为哲学家的毕晓普这只贝克莱大熊指出了用0做除数所具有的矛盾性……而康托尔山羊在它的《普通集合论》里向我们证明了它是如何解决这个问题的，并且消除了数学基础的危机！

2The speed of creating random series used irrational fraction arithmetic was faster than that of multiplicative congruence arithmetic. The correlative value of random series almost was zero.(3) Regarding not harm the images quality as the premise, the speed of FM screening was heightened.

主要结论：利用所建立的条件半色调函数进行图像加网，操作简单、控制精确，使发生阶调不连续处的密度差平均减少到0.01275，明显改善了调幅加网印品的质量；(2)无理数取尾法产生随机数的速度快，数列间几乎没有相关性；(3)在不损失图像质量的前提下，提高了调频加网的输出速度。

The main research methods are:(1)Theory analysis:from the 2D plane geometry analysis, dots continuity characteristics are found. The first time irrational fraction algorithm is used in FM program.(2)Experiments reaearch:experiments of condition halftone function are designed under the cross-experiment principles. The first time variable information printer and C# language are used in experiment.(3)Data processing:new type digital density apparatus is used to measure data. Compare is used in processing data and error cause are explained. The main works as follows:The dot area percentage has been gained and new condition halftone function has been set up.(2)After being corrected, speed of irrational fraction algorithm has been compared with multiplicative congruence algorithm's.

本文的主要研究方法有：(1)理论分析：运用数字加网原理，从二维平面几何分析入手，借助实验验证研究网点连续特性；首次系统地把无理数取尾法随机数生成器引入到调频加网系统中，根据实验修正生成器的模型，运用统计假设检验理论，对生成的随机数序列进行统计假设检验；(2)实验研究：根据正交实验法则设计实验，首次采用可变信息印刷机(HP Laser PS印刷机)输出实验样张，克服了用传统胶印机作实验影响因素多的缺陷；采用新型数字式密度仪测量密度值，提高了数据精度；采用最新编程语言编写调频加网程序；(3)数据处理与分析：利用平均值比较法处理数据，对误差产生的原因进行讨论。

Is an irrational number, also is a transcendental number.

是一个无理数，也是一个超越数。

The square root of two is an irrational number.

二的平方根是一个无理数。

The logical definition of the irrational number is rather sophisticated.

无理数的逻辑主义是颇有些不自然的。

Finally this paper applies the irrational number series to image encryption and gets pleasant encryption effects.

然后将无理数序列应用到图像加密领域，取得了很好的图像加密效果。

The golden ratio is an irrational number close to 1.6181, which when studied has special mathematical properties.

黄金比例是一个无理数接近1.6181 ，具有特殊的数学属性。

The results verify the chaos-like characteristics of irrational number series.

结果表明这些无理数序列与混沌序列具有相似的特性。

For example, you are probably familiar with the number called "pi". This irrational number is so important that we give it a name and a special symbol!

例如，你可能对圆周率"Pi"这个数很熟悉，这个无理数如此重要，以至于我们给它命名，而且用一个特殊符号表示它。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。