汉诺塔游戏

几何画板及绘图内容加载中，请稍等……

2019-08-16 06:14

数列几何作图滑块动画

这个范例演示了汉诺塔游戏的几何构造。它涉及递归和数列的概念。通过使用GeoGebra命令如Sequence，用户可以模拟游戏过程，理解递归关系和数列增长。适合初中及以上学生学习递归和数列。

GeoGebra 命令及参数

Sequence(Polygon[(2 - (2 * Element[seqA, i] / num), (4 * (Length[seqA] - i) / num)), (2 + (2 * Element[seqA, i] / num), (4 * (Length[seqA] - i) / num)), (2 + (2 * Element[seqA, i] / num), (4 * (Length[seqA] - i + 1) / num)), (2 - (2 * Element[seqA, i] / num), (4 * (Length[seqA] - i + 1) / num))], i, 1, Length[seqA]) → discA
Sequence(Polygon[(12 - (2 * Element[seqC, i] / num), (4 * (Length[seqC] - i) / num)), (12 + (2 * Element[seqC, i] / num), (4 * (Length[seqC] - i) / num)), (12 + (2 * Element[seqC, i] / num), (4 * (Length[seqC] - i + 1) / num)), (12 - (2 * Element[seqC, i] / num), (4 * (Length[seqC] - i + 1) / num))], i, 1, Length[seqC]) → discC
Sequence(Polygon[(7 - (2 * Element[seqB, i] / num), (4 * (Length[seqB] - i) / num)), (7 + (2 * Element[seqB, i] / num), (4 * (Length[seqB] - i) / num)), (7 + (2 * Element[seqB, i] / num), (4 * (Length[seqB] - i + 1) / num)), (7 - (2 * Element[seqB, i] / num), (4 * (Length[seqB] - i + 1) / num))], i, 1, Length[seqB]) → discB
Sequence(Polygon[(2 - (2 * Element[tmpA, i] / num), 5), (2 + (2 * Element[tmpA, i] / num), 5), (2 + (2 * Element[tmpA, i] / num), 5 + 4 / num), (2 - (2 * Element[tmpA, i] / num), 5 + 4 / num)], i, 1, Length[tmpA]) → discTA
Sequence(Polygon[(7 - (2 * Element[tmpB, i] / num), 5), (7 + (2 * Element[tmpB, i] / num), 5), (7 + (2 * Element[tmpB, i] / num), 5 + 4 / num), (7 - (2 * Element[tmpB, i] / num), 5 + 4 / num)], i, 1, Length[tmpB]) → discTB
Sequence(Polygon[(12 - (2 * Element[tmpC, i] / num), 5), (12 + (2 * Element[tmpC, i] / num), 5), (12 + (2 * Element[tmpC, i] / num), 5 + 4 / num), (12 - (2 * Element[tmpC, i] / num), 5 + 4 / num)], i, 1, Length[tmpC]) → discTC

AI 绘图提示语参考

绘制汉诺塔游戏的示意图，包含三根竖直的柱子，分别位于左侧、中间和右侧。每根柱子上堆叠着若干圆盘，圆盘从下到上逐渐变小，颜色或形状可区分。左侧柱子的圆盘数量最多，中间和右侧柱子可能为空或部分堆叠。圆盘以矩形或梯形表示，宽度与所在柱子的圆盘大小对应。整体布局水平排列，柱子底部对齐，圆盘垂直堆叠。可添加滑块或动画效果，展示圆盘在柱子间移动的过程，体现递归和序列变化。

以上提示语为根据原始绘图命令整理而来，仅供参考。