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处理空间角与空间距离的计算问题,不仅要对有关“角”与“距离”的概念了如指掌,而且还要善于开动思维机器,灵活调遣线面关系,对问题交错进行设想、论证、转化和计算。所谓转化,就是将隐晦的问题转化为明确的问题,将立体几何的问题转化为平面几何问题等。对于空间角与空间距离的计算,通常是通过构造一个三角形(或四面体),转化为计算三角形(四面体)的边、角、高的问题。构造一个什么样的三角形(四面体)?当然,所求的角或距离应纳入该三角形(四面体)之中,可是,仅满足这点要求的三角形(四面体)往往有多种多样,这就存在一个选择的问题,也就是凭直觉和经验进行设想的问题。
The problem of dealing with the calculation of spatial angles and spatial distances is not only to be familiar with the concepts of “angle” and “distance”, but also to be good at starting up thinking machines, flexibly deploying line relations, and imagining, demonstrating, transforming, and calculating cross-cutting issues. . The so-called transformation is the transformation of hidden issues into clear issues, transforming the problems of solid geometry into plane geometry problems. The calculation of space angles and space distances is usually done by constructing a triangle (or tetrahedron) into the problem of calculating the sides, angles, and heights of a triangle (tetrahedron). What kind of triangle (tetrahedron) is constructed? Of course, the desired angle or distance should be included in the triangle (tetrahedron), but only the triangles (tetrahedron) satisfying this requirement are often varied. There is a question of choice, that is, the question of envisaged intuition and experience.