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汉诺塔问题演示

汉诺塔问题演示
几何画板及绘图内容加载中，请稍等……
2022-01-24 11:38
数列几何作图
①本范例演示汉诺塔问题的解法与过程，通过移动圆盘展示不同层数下的最优移动路径；②涉及的核心数学概念包括递归算法、逻辑推理、序列生成与几何可视化；③作图要点提炼自GeoGebra命令：使用Sequence命令生成序列对象seqC、seqB、seqA，创建按钮、滑块、文本等元素，并利用tmpA、tmpB、tmpC等临时对象实现圆盘移动动画；④适合高中及以上数学学习者，用于理解递归思想、算法设计及几何动态演示。

GeoGebra 命令及参数

  1. 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, {1.777777777777777, 3.5555555555555545, 5.333333333333333}
  2. 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, {}
  3. 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, {}
  4. 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, {}
  5. 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, {}
  6. 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

绘制三根并排的塔架位置，在塔架上方依次生成一组四边形“圆盘”并随序列从左塔到右塔再到中塔出现运动路径的演示。圆盘的左右外形为由四个点构成的矩形轮廓，其中心随不同塔的位置在水平方向平移，且随层数从下到上逐级变窄。给出三个基本圆盘序列分别对应左塔、中塔、右塔：左塔在起始高度自上而下生成一组较窄到较宽的圆盘，中塔与其同形但水平居中，右塔同形但水平偏右。再额外生成三组临时圆盘序列放在固定高度处，作为移动时的过渡位置，从左塔、右塔、中塔分别计算并逐层排列，突出移动过程的几何可视化。
以上提示语为根据原始绘图命令整理而来，仅供参考。