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《300个最新世界著名数学智力趣题》(董莉等编著,哈尔滨出版社1995年出版)中有这样一道题:半径为1的圆盘(包括圆周和圆的内部)上任意放置7个点,使其中任意两个点的距离都不小于1,则7个点中必有一点恰好放在圆心上.直接证明不容易,我们采用反证法.假设上述结论不成立,即7个点都不放在圆心,只须证明,这时7个点中至少存在两个点其距离小于1.而这与题设条件相矛盾,因此待证结论成立.如何证明呢?遇到与个数有关的“存在性”
The 300 most recent world famous mathematical puzzle (edited by Dong Li et al., Published by Harbin Publishing House in 1995) has the following question: Randomly place 7 points on a circle with a radius of 1 (including the inside of a circle and a circle) , So that the distance between any two points are not less than 1, then 7 points must be on the center of a circle. Direct proof is not easy, we use the anti-card method. Assuming the above conclusion is not established, that is, 7 points are not on The center of the circle, only to prove that at this time there are at least two points in the seven points of its distance less than 1. And this is contradictory with the title conditions, the pending conclusion holds. How to prove it? Encountered with the number of “existence Sex ”