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对称是数学美的最基本表现形式之一,这种美不仅给予我们在欣赏和陶冶之时的愉悦之感,还能启迪我们的思维,引领我们的解题方向.所以,我们在解题时,要注意观察数式和几何图形中存在的对称,建立已知和未知之间的联系,从而找到解决问题的突破口.有时问题中可能不能直接表现出一种对称,这就需要我们挖掘题目中的隐含条件,发现寻找对称,从而巧妙地解决问题.我们把这种利用对称的解题思想称之为对偶原则,下面仅举几例,以借读者感悟.
Symmetry is one of the most basic manifestations of mathematical beauty. This beauty not only gives us a sense of euphoria when we admire and mold it, but also enlightens our thinking and guides us in solving problems. Therefore, when we solve problems, Attention should be paid to observing the symmetry existing in the number and geometry, and establish the connection between known and unknown, so as to find a breakthrough to solve the problem. Sometimes the problem may not directly show a kind of symmetry, which requires us to explore hidden issues in the topic. Contains conditions, found to find symmetry, and thus cleverly solve the problem. We call this symmetry of the problem-solving ideas dubbed principle, the following only to mention a few cases, to lend the reader to comprehend.