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一、什么是将军饮马问题将军饮马问题是这样的,传说古希腊的亚历山大城有一位精通数学和物理的学者,名叫海伦。一天,一位将军专程去拜访他,向他请教一个百思不得其解的问题。就是,将军每天要从山峰下的军营A出发,先到河边饮马,然后再到河岸同侧的军营B地开会,应该怎样走才能使路程最短?(如图1)据说这个问题,海伦略加思索就给出了解答(如图2)。从此,这个被称为“将军饮马”的问题就广为流传。这个问题可归纳为如下模型:在平面内给定一条直线L,以及在直线同侧的任意两点A,B,求在L上的点C,使CA+CB取得最小值。这个问题中运用了对称性思想,并化折线段
First, what is the general problem of drinking horses General issue of drinking horses is this, the legendary city of Alexandria in ancient Greece there is a master mathematical and physical scholars, called Helen. One day a general made a special trip to visit him and asked him a baffled question. That is, the general should start daily with barracks A at the summit, drink horses at the riverside, and then meet at the barracks B on the same side of the river bank. How should we go to make the shortest possible distance? (Figure 1) Helen Slightly thought to give the answer (Figure 2). Since then, this is known as the “General Yin Yinma” issue is widely circulated. This problem can be summarized as the following model: Given a straight line L in the plane and any two points A, B on the same side of the line, find the point C on L, which minimizes CA + CB. The problem is the use of symmetry, and broken line segment