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转来信箱栏目的学生来信,内容如下：“周教授：您好!我是贵刊一名忠实读者。经一位老师介绍,有两个问题想向您请教。一是在△ABC中BD、CE为∠B、∠C的平分线,交AC、AB于D、E且BD=EC,求证：AB=AC。这道题我见过两种证法,但都用的是反证法,我的问题是对于此题有没有什么“纯粹”的平面几何证法? 二是关于笔算的。以前从一位老师那学了套笔算开平方的方法,感觉很神奇,相信您也知道。但我就是搞不明白其中的原理,您能
The letters from the students who came to the mail box are as follows: “Prof. Zhou: Hello! I’m a loyal reader of your journal. After one teacher introduced, there are two questions I would like to ask you. The first is in BD, CE is the bisecting line for ∠B, ∠C, AC, AB for D, E and BD = EC, verification: AB = AC. I have seen two kinds of proofs in this question, but all use the anti-evidence method. The question is whether there is any “pure” planar geometrical proof for this question? The second is about the calculation of pens. In the past, a teacher learned the method of writing a square in a set of pens, and it feels amazing. I believe you know it, but I’m Do not understand the principle, you can