一个长方体小盒,(如图1)长AB=4厘米、宽BC=5厘米、高BF=3厘米,一只小蚂蚁从长方体的顶点A出发,经长方体表面爬到与之相对的顶点G,小蚂蚁经过的最短路程是多少?解析这是一类常见的曲面转平面的问题,要想解决此类问题我们通过某处变化,曲面变成平面,再利用“两点之间线段最短”这一公理来解决问题.例如:我们可以把矩形 A cuboid box, (Figure 1) long AB = 4 cm, width BC = 5 cm, high BF = 3 cm, a small ant starting from the apex of the cuboid A, climbed through the cuboid surface to the opposite vertex G , What is the shortest distance that the small ants pass? Analyze This is a kind of common surface turn plane problem, in order to solve such problems, we change somewhere, the surface becomes flat, and then use the “shortest line between two points ”For example: We can put the rectangle