寻求多面体和旋转体上两点之间的最短路径,可以充分利用其侧面展开图,将立体问题平面化,现略举几例.例1如图1,已知正四面体A―BCD,其棱长为1,P、Q分别为AB、CD上的两点,且AP=CQ=λ(0<λ<1),求在四面体侧面上从P到Q的最短距离.解由对称性可知,在侧面上P到Q只须考虑以下两种情况:(1)经过棱AC上一点到达Q; Seeking the shortest path between two points on a polyhedron and a rotating body, we can make full use of its side expansion plan, the three-dimensional problem of planarization, is now a few examples.Example 1 As shown in Figure 1, known tetrahedron A-BCD, the edge Length is 1, P and Q are the two points on AB and CD respectively, and AP = CQ = λ (0 <λ <1), find the shortest distance from P to Q on the side of tetrahedron. , On the side of P to Q only need to consider the following two cases: (1) AC through a point to reach Q;