绕锥一周最短距离的补注

• 作 者: 薛胜保
• 机 构: 山西新绛中学,
• 出 处: 中学数学
• 发表日期: 1987年12期
• 关键词: 最短距离 补注 三棱锥

已知三棱锥S-ABC,自顶点A出发,绕侧面一周再回A点。求最短距离。对这一道常见习题,一般书刊上的解答是,从棱SA处,展其侧面成多边形SABCA＇(图1),则线段AA＇的长为所求。细思之,答案不全面,应这样讨论: 一、若∠A＇SA<130° 1) ∠SAB<∠SAA＇∠SA＇C<∠SA＇A(=∠SAA＇)时,如图2,所求的最短距离为

It is known that the triangular pyramid S-ABC starts from the vertex A and goes back to the point A around the side. Find the shortest distance. For this common problem, the answer in general books and publications is that from the edge SA, the side of the exhibition is a polygon SABCA’ (Figure 1), and the length of the line AA’ is required. Thinking carefully, the answer is not comprehensive, and should be discussed as follows: I. If A’SA<130° 1) ∠SAB<∠SAA’∠SA’C<∠SA’A(=∠SAA’), Figure 2 The shortest distance required is