河内塔 3D 互动演示
2020-12-16 15:51
本 GeoGebra 范例展示了经典的河内塔（Tower of Hanoi）3D 互动模型。用户可以通过界面操作圆盘在三个柱子之间移动，遵循每次只能移动一个圆盘且大盘不能放在小盘上的规则。该模型利用多边形和序列命令构建了立体视觉效果，并实时记录移动步数与圆盘数量。此演示不仅直观呈现了递归算法与数列规律，还帮助学习者深入理解指数增长与逻辑推理在数学谜题中的应用。
所属专题
用GeoGebra制作数学游戏
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遊戲目標是將所有金盤全部移動至另一根銀棒，移動過程必須遵守
以下規定：

 1) 一次只能移動一個金盤。
 2) 只能拿取每根銀棒上最上面的金盤，並放到另一銀棒上。
 3) 較大的金盤不能堆疊在小的金盤之上。

遊戲方式：點擊銀棒或台座，可拿起或放置金盤

The objective of the puzzle is to move the entire stack to another rod,
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 1) Only one disk can be moved at a time.
 2) Each move consists of taking the upper disk from one of the stacks 
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 3) No larger disk may be placed on top of a smaller disk.

How to play: click or tap the plate/rod to take or place the disk. 
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<selectionAllowed val="false"/>
<ggbscript val="If[tmp=={}&&seqC!={},SetValue(tmpC,Insert(tmpC,{Min(seqC)},1))]
If[tmp=={}&&seqC!={},SetValue(seqC,Remove(seqC,{Min(seqC)}))]

If[tmp!={}&&(seqC=={}||Min(seqC)>Min(tmp)),{SetValue(tmpA,{}),SetValue(tmpB,{}),SetValue(tmpC,{})}]
If[tmp!={}&&(seqC=={}||Min(seqC)>Min(tmp)),SetValue(seqC,Insert({Min(tmp)},seqC,1))]

SetValue(tmp,Join(tmpA,tmpB,tmpC))"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<listType val="quadriclimited"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="discA" exp="{Cylinder[(0, 4, 5), (0, 4, 5.5), (tmpA(1) + 1) / 3]}" />
<element type="list" label="discA">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="discB" exp="{Cylinder[((2 * sqrt(3)), -2, 5), ((2 * sqrt(3)), -2, 5.5), (tmpB(1) + 1) / 3]}" />
<element type="list" label="discB">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="discC" exp="{Cylinder[((-2 * sqrt(3)), -2, 5), ((-2 * sqrt(3)), -2, 5.5), (tmpC(1) + 1) / 3]}" />
<element type="list" label="discC">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="textMoves" exp=""完成 " + n + " 個金盤的河內塔，最少需移動 " + mm + " 次。
The minimal number of moves required to
solve a Tower of Hanoi puzzle with " + n + " disks
is " + mm + " times.

目前，您已經移動了 " + moves + " 次。
Now, You have moved " + moves + " times.

電腦：用滑鼠右鍵拖曳視角
觸控裝置：用兩指拖曳視角
PC: Drag with right-mouse-button to spin
Touch Device: Drag with two-finger to spin"" />
<element type="text" label="textMoves">
<show object="true" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="6"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1" size="0" style="1"/>
<absoluteScreenLocation x="38" y="196"/>
</element>
</construction>
</geogebra>