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所谓平面区域Q复盖平面区域T,即是说,T的每一个点都在O内。很显然,平面上面积为S的固定区域能用n个面积分别是S_1,S_2,…,S_n的区域完全复盖的必要条件是S_1+S_2+…+S_n≥S。但是,反过来,s_l+s_2十…s_n≥s时,这n个区域s_1,s_2,…,S_n的全体却未必能完全盖住区域S。比如,无论你怎样摆弄两个壹分的硬币都不可能盖住一个贰分的硬币,尽管两个壹分币的面积之和大于一个贰分币的面积!下面我们给予这个问题的逻辑证明。例1 求证一个直径为1的圆不可能被两个直径小于1的圆所盖住。分析:由于直径为1的圆,在任何一个方向上的
The so-called planar area Q covers the planar area T, that is, every point of T is within O. Obviously, the necessary condition for the complete coverage of a fixed area with an area S on the plane with n areas of S_1, S_2,..., S_n is S_1+S_2+...+S_n≥S. However, when s_l + s_2 ... s_n ≥ s is reversed, the entire area n of the n regions s_1, s_2, ..., S_n may not completely cover the region S. For example, no matter how you play with two coins, it is impossible to cover a coin. Although the sum of the area of two coins is more than one coin area, we will give a logical proof of this problem. Example 1 Verify that a circle with a diameter of 1 cannot be covered by two circles with a diameter less than 1. Analysis: Due to the diameter of 1 circle, in any direction