向量的闭合回路在问题解决中的巧妙运用

• 作 者: 孙芸
• 机 构: 江苏省海门中学,
• 出 处: 数学通讯
• 发表日期: 2014年Z1期
• 关键词: 闭合回路 问题解决 数学问题 首尾相接 数量积 化繁为简

所谓“向量的闭合回路”就是向量从一点出发,通过一个封闭的图形又回到原点的那个通路.显然,n个向量构成闭合回路的条件是相邻两个向量都必须首尾相接,其代数形式是→A1A2+→A2A3+…+→AnA1=0.解数学问题时,如果从“向量的闭合回路”切入思维,往往会找到解题突破口,并起到化繁为简、化难为易的效果.下面从八个方面举例说明“向量的闭合回路”在问题解决中的巧妙运用.

The so-called “closed loop” of a vector is the path from which the vector returns from a point to the origin through a closed graph.Obviously, the condition that n vectors form a closed loop is that two adjacent vectors must be connected end to end, The algebraic form is → A1A2 + → A2A3 + ... + → AnA1 = 0. When solving mathematical problems, if we cut into the thinking from the closed loop of the vector, we often find a breakthrough point for solving the problem, Easy to effect the following eight examples from the “closed loop vector” in the problem-solving clever use.