论文部分内容阅读
1问题来源高中练习题中,有一个常见问题:与三棱锥S-ABC四个顶点的距离相等的平面有几个?常见解答:所求平面必须将四个顶点分隔在两侧,情况一:平面两侧各有两个顶点,形成一对异面直线,到它们距离相等的平面即为所求,如图1,这样的平面共有C242=3个;情况二:平面两侧顶点数分别为1个和3个,中截面即为所求,如图2,这样的平面共有C14=4个.所以总共有7个不同的平面符合要求.图1
1 Problem Source High School Exercises There is a common question: How many planes are at equal distances from the four vertices of S-ABC? Common Answers: The plane to be solved must have four vertices separated on both sides. Case 1: There are two vertices on each side of the plane, forming a pair of straight lines with different planes, that is, the distance from them to the plane of equal distance is as shown in Figure 1. There are totally C242 = 3 planes in this plane. Case 2: 1 and 3, the cross-section is the desired, as shown in Figure 2, such a total plane C14 = 4. So a total of seven different planes meet the requirements. Figure 1