一什么是抽屉原则把4本书分放在3个抽屉内,至少有一个抽屉内放2本或2本以上的书,这就是“抽屉原则”,我们把“抽屉”看成“集合”,而把“书”看作“元素”,抽屉原则可叙述为: 旅则1 把多于n个的元素按任一确定的方式分成n个集合,那么一定有一个集合中含有两个或两个以上的元素。(其正确性很容易用反证法证得。) 就是这样一个简单的事实,在初等数学中有着广泛的应用,特别是数学中一类“存在性”问题经常用到“抽屉原侧则”。例1 在圆内或圆上任取8个点,证明:在这8个点甲,必有两个点的距离小于圆的半径。证明:在所取的8个点中,至少有7个点不和圆 What is the principle of a drawer? Put four books in three drawers. At least one drawer contains two or more books. This is the “drawer principle”. We regard “drawers” as “collections.” Considering “book” as “element”, the principle of drawer can be described as: Brigade 1 divides more than n elements into n sets in any definite way, then there must be one set containing two or two The above elements. (The correctness is easily proved by counter-evidence.) It is such a simple fact that it has a wide range of applications in elementary mathematics. In mathematics, one type of “existence” problem often uses the “original drawer”. Example 1 Take 8 points in a circle or on a circle to prove that: At these 8 points, there must be two points less than the radius of the circle. Proof: Among the 8 points taken, at least 7 points do not coincide with the circle