论文部分内容阅读
高三代数书上介紹賈先三角形,粗看起来內容不多,其实大可研究。茲以实例說明。 (一)課本上提到在賈宪三角形里面除1以外的每一个数都等于它肩上两个数的和,我就抓住这一道理,通过图解首先让同学牢固掌握課本第9頁[例2]C_m~n+C_m~(n+1)=C_(m+1)~(n+1)这一組合性貭。(图解見图1) 在掌握这一图解法的基础上,我帮助同学拓展知識領域,先把C_m~n+C_m~(n+1)=C_(m+1)~(n+1)改写为C_1~1·C_m~n++C_1~0·C_m~(n+1)=C_0~0·C_(m+1)~(n+1)的形式,而在“图1”中以C_m~n,C_m~(n+1)C_(m+1)~(n+1)为頂点的三角形适巧与以C_1~1,C_1~0,C_0~0为顶点的三
The third-generation algebra book introduces Jia Xian’s triangle. The rough content does not seem to be much. In fact, it can be studied. Here is an example. (1) The textbook mentions that each number other than one in the triangle of Jia Xian equals the sum of two numbers on its shoulder. I seize this principle and let the students firmly grasp the textbook page 9 [ Example 2] The combination of C_m~n+C_m~(n+1)=C_(m+1)~(n+1). (Illustration is shown in Figure 1.) Based on this graphic method, I help my classmates expand their knowledge field by first rewriting C_m~n+C_m~(n+1)=C_(m+1)~(n+1). Is in the form of C_1~1·C_m~n++C_1~0·C_m~(n+1)=C_0~0·C_(m+1)~(n+1), while in the “Fig. 1” C_m ~n, C_m~(n+1)C_(m+1)~(n+1) is the triangle of the vertices and three with C_1~1, C_1~0, C_0~0 as the vertices