在中学数学里,讲无理数概念前,先讲循环小数化分数的方法,以此证明循环小数可以化为分数。但问题的另一方面,即分数为什么可以化为有限小数或循环小数却没讲。其实,利用鸽笼原理的初等形式,是可以很容易地讲清此问题的。 鸽笼原理 将n+1只鸽子放入n个鸽笼内,则至少有一鸽宠内含有两只或两只以上的鸽子。 In middle school mathematics, before speaking about the concept of irrational numbers, we first talk about the method of recycling fractionalized scores to prove that looping fractions can be converted into fractions. But the other side of the question is why fractions can be reduced to finite decimals or loops. In fact, using the primary form of the pigeon cage principle, this problem can be easily explained. Columbine principle When n+1 pigeons are placed in n pigeonholes, at least one dove pet contains two or more pigeons.