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一、问题的提出G·波利亚有一句名言“掌握数学就意味着善于解题”。解决数学问题时,常规的思考方法是由已知到未知的定向思考,但有些问题按照这样的思维方式来解决问题却比较困难,甚至无从着手。在这种情况下,就要求我们改变思维方向,换一个角度去思考,找到一条绕过障碍的新途径。构造法就是这样的手段之一。G·波利亚在他的《怎样解题》中给出了“怎样解题”表,其中第二步是拟定计划,“找出已知数与未知数之间的联系。如果找不出直接的联系,你可能不得不考虑辅助问题。”运用辅助性数学模式,这也正是我们用构造法解决问题的思路。构造法的特点:构造新的数学对象过程直观,有很大灵活性。
First, the issue put forward G · Polia has a famous saying “mastery of mathematics means good problem-solving.” When solving mathematical problems, the conventional way of thinking is from the known to the unknown oriented thinking, but some problems in accordance with this way of thinking to solve the problem is more difficult, or even impossible. Under such circumstances, we are required to change our thinking direction and think from a different angle and find a new way to get around the obstacles. Construction method is one of such means. In his “How to Solve Problems,” G. Poliah gives the “How to Solve Problems” table, where the second step is to draw up a plan to “find out the connection between known and unknown numbers. No direct connection, you may have to consider auxiliary problems. ”The use of auxiliary mathematical model, which is the way we use constructs to solve the problem. The characteristics of the construction method: Constructing a new mathematical object is intuitive and flexible.