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众所周知,数学来源于实践,又反作用于实践.在现实生活中,经常会遇到最优方案,最少费用,材料最省等问题.这些问题通常需要建立数学模型解决,本文就最短路径问题分成四种情况,分别建立数学模型,进行研究,并辅以练习,期望对读者有所启发.一、利用轴对称的性质求“两点在一条直线异侧”的最小值问题如图1,已知,点AB分别是直线l异侧的两个点,在l上找到一点C,使AC+BC最小.
As we all know, mathematics comes from practice, but also counteract in practice.In practice, we often encounter the optimal solution, the least cost, the least material and so on.Most of these problems usually need to be solved by the mathematical model.This paper divided the shortest path problem into four Kind of situation, respectively, to establish a mathematical model, research, supplemented by practice, expect to be inspired by the reader. First, the use of the nature of axial symmetry “two points in a straight line ” the minimum problem shown in Figure 1, It is known that points AB are the two points on the opposite side of line l, respectively, and find a point C on l to minimize AC + BC.