论文标题
如何很好地近似非理性数字？
How to approximate irrational numbers nicely?
论文作者
论文摘要
在文献中，我们有多种证明实际数字不合理的方式。在这篇调查文章中，我们将强调特定的标准以证明非理性。这称为按一系列有理数的数字近似值。这种非理性标准很容易证明，并且非常重要。使用它，证明了大量数字的不合理性。我们将使用这种方法来证明代数，指数和三角非理性数字的非理性性。在大多数情况下，明确的构造都是由一个不错的理性数字序列完成的。所使用的参数是基本的，例如函数的二项式定理，最大值和最小值。因此，本科生可以访问这篇调查文章，并为任何寻求娱乐数学的人都有广泛的吸引力。本文在不使用任何重量级机械的情况下展示了古典知名的美丽数学。
In the literature, we have various ways of proving irrationality of a real number. In this survey article, we shall emphasize on a particular criterion to prove irrationality. This is called nice approximation of a number by a sequence of rational numbers. This criterion of irrationality is easy to prove and is of great importance. Using it, irrationality of a large class of numbers is proved. We shall apply this method to prove irrationality of algebraic, exponential and trigonometric irrational numbers. Most of the times, explicit constructions are done of the nice sequence of rational numbers. Arguments used are basic like the binomial theorem and maxima and minima of functions. Thus, this survey article is accessible to undergraduate students and has a broad appeal for anyone looking for entertaining mathematics. This article brings out classically known beautiful mathematics without using any heavyweight machinery.
