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将正$4k$边形划分成若干平行四边形证至少有$k$个矩形

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isee posted 2018-1-6 16:30 |Read mode
将一个边长为$a$的正$4k$边形划分成若干平行四边形。
证明:在这些平行四边形中,至少有$k$个矩形,并求这些矩形面积之和(用$k$和$a$表示)。

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