Construction and Demonstration of Vector Arrays
2020-10-09 17:45
This example demonstrates how to construct 2D vector arrays using the Flatten and Sequence commands in GeoGebra. By defining base points and vectors, combined with sequence and list operations, a regularly arranged set of vectors is generated. This demonstration helps in understanding the geometric interpretation of vectors, linear combinations, and the application of geometric transformations in
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1. 周期为4的点列，先做出第一个周期的四个点A、B、C、D\\
2. 四点打包成一个列表 list1={A,B,C,D} 按顺序放置\\
3. 制作一个平移向量 u = (4,0), 周期为4的缘故\\
4. 制作一个控制平移次数的滑块 n=Slider(0,30,1)\\
5. 巧妙利用序列命令产生系列点阵 l2=Sequence(Translate(l1, k*u),k=0,n)\\
6. 上述产生的点列是二维的，需要扁平化 l2=Flatten(l2)\\
7. 构造向量阵列 l3=Sequence(Vector(l2(k),l2(k+1)),k,0,length(l2))\\
 这里的 l2(k) 表示 列表l2中的第k个元素（点），\\
 也可以改成不会产生歧义的的命令 Element(l2,k)\\
8. 改变滑动条n，即可看到动态生成效果。\\
9. 增加点坐标阵列显示 l3=Sequence(Text(l2(k), l2(k)), k, 0, Length(l2))""/>
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