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众所周知,杨辉三角是我国古代数学的一个杰出成就,是中华古代文明的骄傲。杨辉三角是数学的一个宝库,组合数的很多性质都蕴藏在这个宝库之中。近年,人们研究了杨辉三角的几何图案。如图1所示,在杨辉三角中,在奇数处画一个黑色正方形,在没有数或偶数处保持空白,就能得到几何图案。图2是用上述方法得到的杨辉三角头64行的几何图案,非常美观,妙不可言。而且,人们很容易发现它的规律,从而可以继续无限地画下去。但对这样的规律给出证明,那就十分
As we all know, the Yanghui Triangle is an outstanding achievement of ancient Chinese mathematics and it is the pride of ancient Chinese civilization. Yang Hui Triangle is a treasure house of mathematics. Many properties of the combination number are hidden in this treasure house. In recent years, people have studied the geometric pattern of Yang Hui triangle. As shown in Fig. 1, in the Yang Hui triangle, a black square is drawn at odd numbers and a geometric pattern can be obtained if there is no number or even number of blank squares. Figure 2 is a geometric pattern of the Yanghui triangle head obtained by the above method, which is very beautiful and wonderful. Moreover, it is easy for people to find out its laws so that they can continue to paint indefinitely. But to prove such a law, it is very