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在數學通報1954年10月號內登載了潘關崇同志的“幾何示教的幾點體會”一篇文章。我們讀了以後,覺得潘關崇同志對於對稱法的講法有很多優點,如從實際出發,並與物理相聯系,注意教材的系統性等等。因而給我們的教學很大啟發,但是我們也感覺到有一點似乎有補充的必要,就是能修水塔的問題時,怎麼就會想到要作點M的對稱點?若不事先作好準備工作,恐怕學生便要發生疑問;因此我們認為可以先提一個問題作為準備。即“在AB河的一側有一村M,而在另一側有一村N,今要在河邊上建築一個自來水塔,使與MN二村為自用水管直接相通,問水塔應築在何處,而所用的直通水管最省?”若以純理論題的形式出現,便可寫成“已知二點M,N在一定直線AB的異側;於AB上求一點P,使MP+PN為最小。”我們認為若先解决了這個問題,不但原來的問題不會使學生發生疑問,同時還把有關異側點的問題也教給學生了。
In the October 1954 issue of the Mathematics Bulletin, an article entitled “Some Experiences in Geometry Teaching” by Comrade Pan Guanchong was published. After we read it, I feel that Comrade Pan Guanchong has many advantages for the symmetry method, such as proceeding from reality, linking with physics, and paying attention to the systematic nature of textbooks. This gave us a lot of inspiration for teaching, but we also felt that one thing seemed to be necessary for supplementation. When we were able to repair the water tower, how could we think of the point of symmetry of point M? If we did not make preparations in advance, I am afraid that students will have questions; therefore, we think that it is possible to prepare a question first. That is to say, “There is a village M on one side of the AB River, and a village N on the other side. To build a water tower on the river, it is necessary to connect the MN 2 village directly with the water pipe and ask where the water tower should be built. And if the straight water pipe used is the most provincial?“ If it appears in the form of a pure theoretical problem, it can be written as ”The known two points M, N are on the opposite side of a certain line AB; on AB, a point P is obtained, so that MP + PN is the smallest. "We believe that if this problem is first resolved, not only will the original problem not lead students to question, but it will also teach the students about the problems of the opposite side.