Pentago Board Game Simulation
2021-01-11 00:46
This GeoGebra applet simulates the classic board game Pentago. It uses Polygon and Sequence commands to construct a 6x6 board divided into four rotatable 3x3 quadrants. By leveraging the Rotate command and interactive buttons, it dynamically demonstrates the 90-degree rotation of any quadrant after a piece is placed. This model vividly illustrates the application of geometric transformations in lo
In collections
Math Games with GeoGebra
Loading the GeoGebra board and drawing, please wait…
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<coords x="0.9999999999999997" y="-5" z="1"/>
<pointSize val="25"/>
<pointStyle val="0"/>
</element>
<expression label="Blacks" exp="{(4, 1, 1), (4, 5, 3)}"/>
<element type="list" label="Blacks">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="1"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="Whites" exp="{(3, 5, 1), (3, 1, 1)}"/>
<element type="list" label="Whites">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="1"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<element type="button" label="buttonScript">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="497" y="832"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="If[showTwistButtons==false&&turn==true,SetValue(Blacks,Append(Blacks,F))]
If[showTwistButtons==false&&turn==false,SetValue(Whites,Append(Whites,F))]

SetValue(showTwistButtons,true)"/>
<font serif="false" sizeM="2" size="16" style="0"/>
</element>
<element type="button" label="buttonReset">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="191" g="255" b="0" alpha="255"/>
<layer val="9"/>
<labelOffset x="284" y="806"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(F,(0,0,0))
SetValue(α1,0°)
SetValue(α2,0°)
SetValue(α3,0°)
SetValue(α4,0°)
SetValue(turn,true)
Blacks={}
Whites={}
SetValue(showTwistButtons,false)"/>
<font serif="false" sizeM="3" size="32" style="1"/>
<dimensions width="225" height="80" />
<startPoint x="-2.2" y="-8.2" z="1"/>
<caption val="New Game"/>
</element>
<element type="boolean" label="turn">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="boolean" label="showTwistButtons">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="numeric" label="nBWSize">
<value val="32"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="20" max="40" absoluteScreenLocation="true" width="200" x="18" y="256" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<ggbscript onUpdate="SetPointSize(BlacksC,nBWSize)
SetPointSize(WhitesC,nBWSize)"/>
</element>
<expression label="F" exp="(3, 1, 1)" type="point"/>
<element type="point3d" label="F">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="If[F!=(0,0),RunClickScript(buttonScript)]"/>
<coords x="3" y="1" z="1" w="1"/>
<pointSize val="5"/>
</element>
<command name="Sequence">
<input a0="If[x(Blacks(k)) ≟ 1, O1 + (y(Blacks(k)) * u1) + (z(Blacks(k)) * v1), x(Blacks(k)) ≟ 2, O2 + (y(Blacks(k)) * u2) + (z(Blacks(k)) * v2), x(Blacks(k)) ≟ 3, O3 + (y(Blacks(k)) * u3) + (z(Blacks(k)) * v3), x(Blacks(k)) ≟ 4, O4 + (y(Blacks(k)) * u4) + (z(Blacks(k)) * v4)]" a1="k" a2="1" a3="Length[Blacks]"/>
<output a0="BlacksC"/>
</command>
<element type="list" label="BlacksC">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="SelectObjects()"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="32"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="If[x(Whites(k)) ≟ 1, O1 + (y(Whites(k)) * u1) + (z(Whites(k)) * v1), x(Whites(k)) ≟ 2, O2 + (y(Whites(k)) * u2) + (z(Whites(k)) * v2), x(Whites(k)) ≟ 3, O3 + (y(Whites(k)) * u3) + (z(Whites(k)) * v3), x(Whites(k)) ≟ 4, O4 + (y(Whites(k)) * u4) + (z(Whites(k)) * v4)]" a1="k" a2="1" a3="Length[Whites]"/>
<output a0="WhitesC"/>
</command>
<element type="list" label="WhitesC">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="SelectObjects()"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="32"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="wins" exp="{{(-5, -3), (-5, -1), (-5, 1), (-5, 3), (-5, 5)}, {(-3, -3), (-3, -1), (-3, 1), (-3, 3), (-3, 5)}, {(-1, -3), (-1, -1), (-1, 1), (-1, 3), (-1, 5)}, {(1, -3), (1, -1), (1, 1), (1, 3), (1, 5)}, {(3, -3), (3, -1), (3, 1), (3, 3), (3, 5)}, {(5, -3), (5, -1), (5, 1), (5, 3), (5, 5)}, {(-5, -5), (-5, -3), (-5, -1), (-5, 1), (-5, 3)}, {(-3, -5), (-3, -3), (-3, -1), (-3, 1), (-3, 3)}, {(-1, -5), (-1, -3), (-1, -1), (-1, 1), (-1, 3)}, {(1, -5), (1, -3), (1, -1), (1, 1), (1, 3)}, {(3, -5), (3, -3), (3, -1), (3, 1), (3, 3)}, {(5, -5), (5, -3), (5, -1), (5, 1), (5, 3)}, {(-5, -5), (-3, -5), (-1, -5), (1, -5), (3, -5)}, {(-5, -3), (-3, -3), (-1, -3), (1, -3), (3, -3)}, {(-5, -1), (-3, -1), (-1, -1), (1, -1), (3, -1)}, {(-5, 1), (-3, 1), (-1, 1), (1, 1), (3, 1)}, {(-5, 3), (-3, 3), (-1, 3), (1, 3), (3, 3)}, {(-5, 5), (-3, 5), (-1, 5), (1, 5), (3, 5)}, {(-3, -5), (-1, -5), (1, -5), (3, -5), (5, -5)}, {(-3, -3), (-1, -3), (1, -3), (3, -3), (5, -3)}, {(-3, -1), (-1, -1), (1, -1), (3, -1), (5, -1)}, {(-3, 1), (-1, 1), (1, 1), (3, 1), (5, 1)}, {(-3, 3), (-1, 3), (1, 3), (3, 3), (5, 3)}, {(-3, 5), (-1, 5), (1, 5), (3, 5), (5, 5)}, {(-5, -3), (-3, -1), (-1, 1), (1, 3), (3, 5)}, {(-5, -5), (-3, -3), (-1, -1), (1, 1), (3, 3)}, {(-3, -3), (-1, -1), (1, 1), (3, 3), (5, 5)}, {(-3, -5), (-1, -3), (1, -1), (3, 1), (5, 3)}, {(-3, 5), (-1, 3), (1, 1), (3, -1), (5, -3)}, {(-5, 5), (-3, 3), (-1, 1), (1, -1), (3, -3)}, {(-3, 3), (-1, 1), (1, -1), (3, -3), (5, -5)}, {(-5, 3), (-3, 1), (-1, -1), (1, -3), (3, -5)}}"/>
<element type="list" label="wins">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="RemoveUndefined">
<input a0="Sequence[If[wins(k) ⊆ BlacksC, wins(k)], k, 1, Length[wins]]"/>
<output a0="BlackWin"/>
</command>
<element type="list" label="BlackWin">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<listType val="list"/>
<pointSize val="9"/>
<pointStyle val="3"/>
<angleStyle val="0"/>
</element>
<command name="RemoveUndefined">
<input a0="Sequence[If[wins(k) ⊆ WhitesC, wins(k)], k, 1, Length[wins]]"/>
<output a0="WhiteWin"/>
</command>
<element type="list" label="WhiteWin">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<listType val="list"/>
<pointSize val="9"/>
<pointStyle val="2"/>
<angleStyle val="0"/>
</element>
<element type="button" label="buttonTurnBlack">
<show object="true" label="true"/>
<condition showObject="turn"/>
<objColor r="128" g="128" b="128" alpha="1"/>
<bgColor r="0" g="0" b="0" alpha="255"/>
<layer val="2"/>
<labelOffset x="55" y="801"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="true"/>
<font serif="false" sizeM="4" size="48" style="1"/>
<dimensions width="180" height="80" />
<startPoint x="-6" y="-8" z="1"/>
<caption val="Black"/>
</element>
<element type="button" label="buttonTurnWhite">
<show object="true" label="true"/>
<condition showObject="¬turn"/>
<objColor r="128" g="128" b="128" alpha="1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="2"/>
<labelOffset x="554" y="800"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="true"/>
<font serif="false" sizeM="4" size="48" style="1"/>
<dimensions width="180" height="80" />
<startPoint x="2.5" y="-8" z="1"/>
<caption val="White"/>
</element>
<command name="If">
<input a0="BlackWin ≠ {}" a1="true" a2="false"/>
<output a0="bBlackWin"/>
</command>
<element type="boolean" label="bBlackWin">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="If">
<input a0="WhiteWin ≠ {}" a1="true" a2="false"/>
<output a0="bWhiteWin"/>
</command>
<element type="boolean" label="bWhiteWin">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="Polygon">
<input a0="{Corner[1], Corner[2], Corner[3], Corner[4]}"/>
<output a0="polyMask"/>
</command>
<element type="polygon" label="polyMask">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showTwistButtons ≟ false ∧ (bBlackWin ≠ false ∨ bWhiteWin ≠ false)"/>
<objColor r="0" g="0" b="0" alpha="0.5"/>
<layer val="8"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
</element>
<expression label="a" exp="a: y ≤ -6" type="inequality"/>
<element type="function" label="a">
<show object="true" label="false" ev="4"/>
<condition showObject="showTwistButtons ≟ false ∧ (bBlackWin ≠ false ∨ bWhiteWin ≠ false)"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="8"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<expression label="text1" exp=""Game Over! " + (If[bBlackWin ≟ true ∧ bWhiteWin ≟ true, "Ended with a DRAW.", bBlackWin ≟ true ∧ bWhiteWin ≟ false, "The BLACK wins.", bBlackWin ≟ false ∧ bWhiteWin ≟ true, "The WHITE wins."]) + "
遊戲結束！ " + (If[bBlackWin ≟ true ∧ bWhiteWin ≟ true, "雙方平手..", bBlackWin ≟ true ∧ bWhiteWin ≟ false, "黑方獲勝.", bBlackWin ≟ false ∧ bWhiteWin ≟ true, "白方獲勝."]) + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="8"/>
<condition showObject="showTwistButtons ≟ false ∧ (bBlackWin ≠ false ∨ bWhiteWin ≠ false)"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="8"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="2" size="16" style="0"/>
<startPoint x="-5" y="-6.9" z="1"/>
</element>
</construction>
</geogebra>