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题目呈现(人教版数学必修五113页第2题)如图1,树顶A离地面am,树上另一点B离地面bm,在离地面的C处看此树,离此树多远时视角最大?此题在各种教参、资料上都有详细的解析,但题目丰富的背景与广泛运用却未曾提及.本文将重点介绍该问题的中等数学背景和其在生活、高考与竞赛中的广泛运用,供参考.1、背景探讨题目的本质:一个角的一边上有固定两点,另一边上有一动点,求以动点为顶点,动点与两固定点为边形成角度的最大值.它源于一个著名的数学问题:米勒问题.米勒问题
Topic presentation (PEP mathematics compulsory five 113 page 2) As shown in Figure 1, tree top A from the ground am, tree another point B from the ground bm, at the ground from the C to see this tree, from the tree how far When the perspective of the largest? This question in a variety of teaching parameters, the data have detailed analysis, but the rich background and extensive use has not been mentioned.This article will focus on the mathematical background of the problem and its life, college entrance examination and The extensive use of the competition, for reference .1, background to explore the nature of the subject: a corner of the fixed two points on one side, there is a moving point on the other, seeking the moving point as the vertex, moving point and the two fixed points for the edge It comes from a famous mathematical problem: Miller’s problem, Miller’s problem