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“三村短路”问题就是“如何用一组公路将不在一条直线上的三个村庄连接起来,并且使公路的长度最短”。用数学语言表达即为:“在平面上求一点,使其到三角形三顶点距离之和最小。”该问题的平几证法已有。本文拟用复平面及“ω”的性质给予巧证。
The problem of “three villages short-circuiting” is “how to connect a group of roads to three villages that are not on a straight line, and to minimize the length of the road.” Expressing in mathematics means: “Find a point on the plane to minimize the sum of the distances between the three vertices of the triangle.” This article intends to use the nature of the complex plane and “ω” to give clever evidence.