了解积分——分割的艺术

求一个函数的黎曼积分，实际上就是一个分割、近似代替、求和、取极限的过程．分割是整个过程的初始点．本文以黎曼积分中的分割问题做背景知识，用通俗的语言，而不是严格的数学语言，介绍了分割的过程是如何实现的，应该注意哪些基本问题，整体与局部的联系，如何保证分割是我们期望的、有效的、均匀分割，以及对一个空间的或者集合的分割如何实现等，做了些许描述．为初学者在学习中并应用这样的方法时，应该如何思考问题，如何动手解决问题，进而如何创造新的知识，提供一个可以借鉴的途径．

Know Integrals--Arts of Partitions

Solving a Riemann integral problem is actually a process of partition, summation and limitation. As partition is the fundamental step of the whole process, we make it the basis of introducing the realization of partition by using popular language instead of strict mathematical terms. Some basic problems, like the bond of integer and section, how to do the partition to get expected, effective and uniform one and how to divide a space or a set , ete, have been discussed in the paper to provide a reference for people, especially new learners who are in learning, thinking and solving this kind of problems. Furthermore, it might be some help to creating new knowledge as well.