旋转对称演示
2013-08-16 08:21
本范例动态演示了图形的旋转对称性。通过 GeoGebra 构造，用户可以观察图形绕中心点旋转特定角度后与原图形重合的过程。利用序列、圆、点、角、线段和旋转等命令，直观展示旋转对称的几何特征，帮助深入理解旋转对称的概念及其在几何图形中的性质与应用。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.289.0" id="b256d9c1-f080-4851-8f2e-9c24d152869f" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="960" height="660" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.15151515151515152" orientation="0" />
<pane location="1" divider="0.10416666666666667" orientation="1" />
</panes>
<views>
<view id="1" visible="true" inframe="false" stylebar="false" location="2,1" size="958" window="100,100,600,400" />
<view id="4" toolbar="0 59 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 | 1011 || 1008 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="1" size="654" window="100,100,250,400" />
<view id="16" visible="true" inframe="false" stylebar="false" location="0" size="100" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="true" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="true" stylebar="true" location="1" size="375" window="176,134,928,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="true" stylebar="false" location="1" size="480" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 59 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 66 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="7" help="false" />
<input show="false" cmd="true" top="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="958" height="550"/>
<coordSystem xZero="605.5" yZero="285.99999999999994" scale="41.44369181977479" yscale="41.44369290489085"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="0" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="208" g="240" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="1" distY="1" distTheta="0.5235987755982988"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="958" height="100"/>
<coordSystem xZero="430.8425157248325" yZero="216.12848104016697" scale="34.228287933635976" yscale="34.22828793363592"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="208" g="240" b="192"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="1" distY="1" distTheta="0.5235987755982988"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="1"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="A">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelOffset x="-56" y="-58"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<selectionAllowed val="false"/>
<coords x="0.93" y="4.12" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
<caption val="Start"/>
</element>
<element type="image" label="pic1">
<file name="0de44ded35b58b83df1a36bd90cbff85\HKSAR.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.8293421778214047" y="-3.8293421778214034" z="1"/>
<startPoint number="1" x="4.170657822178596" y="-3.8293421778214034" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="a"/>
<objColor r="0" g="0" b="0" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic2">
<file name="8af23a4a06fd3b1695f51e838fb94868\Eastern_District_Hong_Kong.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="b"/>
<objColor r="0" g="0" b="0" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic3">
<file name="59bbf3bcff6ba5f7dd10f7367422d93e\Kwun_Tong_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<startPoint number="2" x="-4" y="3.9619047619047283" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="c"/>
<objColor r="0" g="0" b="0" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic4">
<file name="7165db8fa971a95daa136147e69613bf\Sham_Shui_Po_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.955854104185652" y="-3.9337811562784792" z="1"/>
<startPoint number="1" x="4.0441458958143475" y="-3.9337811562784792" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="0" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic5">
<file name="5da28394bd19f4370249b4c67c485964\Shatin_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.9779270520928267" y="-3.889635260464132" z="1"/>
<startPoint number="1" x="4.022072947907173" y="-3.889635260464132" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="e"/>
<objColor r="0" g="0" b="0" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic6">
<file name="dba09a41e755216805c195f4939ed447\Tsuen_Wan_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic7">
<file name="c40759008829375adb1ce483627c5cb4\Tuen_Mun_District.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="g"/>
<objColor r="0" g="0" b="0" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic8">
<file name="87c3484c1e17fc2ac18e64af6161a923\Wong_Tai_Sin District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.9779270520928263" y="-4.088291791628695" z="1"/>
<startPoint number="1" x="4.022072947907174" y="-4.088291791628695" z="1"/>
<startPoint number="2" x="-3.9779270520928263" y="3.9117082083712713" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="h"/>
<objColor r="0" g="0" b="0" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic9">
<file name="7bd025efea0f16552990c8b201bd5119\Yau_Tsim_Mong_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="i"/>
<objColor r="0" g="0" b="0" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="boolean" label="a">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="15" y="6"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[b,false] SetValue[c,false] SetValue[d,false] SetValue[e,false] SetValue[f,false] SetValue[g,false] SetValue[h,false] SetValue[i,false] SetValue[A,If[a,(0.93,4.12),A]] SetValue[B,A]"/>
<caption val="Figure 1"/>
</element>
<element type="boolean" label="b">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="152" y="6"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[c,false] SetValue[d,false] SetValue[e,false] SetValue[f,false] SetValue[g,false] SetValue[h,false] SetValue[i,false] SetValue[A,If[b,(1.72,4.01),A]] SetValue[B,A]"/>
<caption val="Figure 2"/>
</element>
<element type="boolean" label="c">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="289" y="6"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[d,false] SetValue[e,false] SetValue[f,false] SetValue[g,false] SetValue[h,false] SetValue[i,false] SetValue[A,If[c,(1.7,3.96),A]] SetValue[B,A]"/>
<caption val="Figure 3"/>
</element>
<element type="boolean" label="d">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="426" y="6"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[c,false] SetValue[e,false] SetValue[f,false] SetValue[g,false] SetValue[h,false] SetValue[i,false] SetValue[A,If[d,(3.68,3.59),A]] SetValue[B,A]"/>
<caption val="Figure 4"/>
</element>
<element type="boolean" label="e">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="563" y="6"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[c,false] SetValue[d,false] SetValue[f,false] SetValue[g,false] SetValue[h,false] SetValue[i,false] SetValue[A,If[e,(3.68,3.59),A]] SetValue[B,A]"/>
<caption val="Figure 5"/>
</element>
<element type="boolean" label="f">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="700" y="6"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[c,false] SetValue[d,false] SetValue[e,false] SetValue[g,false] SetValue[h,false] SetValue[i,false] SetValue[A,If[f,(0,4),A]] SetValue[B,A]"/>
<caption val="Figure 6"/>
</element>
<element type="boolean" label="g">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="15" y="40"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[c,false] SetValue[d,false] SetValue[e,false] SetValue[f,false] SetValue[h,false] SetValue[i,false] SetValue[A,If[g,(0,4.94),A]] SetValue[B,A]"/>
<caption val="Figure 7"/>
</element>
<element type="boolean" label="h">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="152" y="40"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[c,false] SetValue[d,false] SetValue[e,false] SetValue[f,false] SetValue[g,false] SetValue[i,false] SetValue[A,If[h,(0,3.92),A]] SetValue[B,A]"/>
<caption val="Figure 8"/>
</element>
<element type="boolean" label="i">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="289" y="40"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[c,false] SetValue[d,false] SetValue[e,false] SetValue[f,false] SetValue[g,false] SetValue[h,false] SetValue[A,If[i,(4,4),A]] SetValue[B,A]"/>
<caption val="Figure 9"/>
</element>
<command name="Sequence">
<input a0="Rotate[A, i°]" a1="i" a2="1" a3="360"/>
<output a0="list1"/>
</command>
<element type="list" label="list1">
<show object="false" label="false"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="3"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="1"/>
<pointStyle val="-1"/>
</element>
<element type="point" label="O">
<show object="true" label="false"/>
<condition showObject="select"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<coords x="0" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="1"/>
</element>
<command name="Circle">
<input a0="O" a1="A"/>
<output a0="k"/>
</command>
<element type="conic" label="k">
<show object="true" label="false"/>
<condition showObject="showAngle"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="3" type="10" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-17.839299999999998" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="list1"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="false" ev="4"/>
<condition showObject="select"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="-12" y="41"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0.930000000000001" y="4.12" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
<caption val="Drag"/>
</element>
<command name="Angle">
<input a0="B" a1="O" a2="A"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="0"/>
<value val="0"/>
<show object="false" label="false" ev="4"/>
<condition showObject="showAngle"/>
<objColor r="0" g="100" b="0" alpha="0.5"/>
<layer val="2"/>
<labelOffset x="-50" y="-62"/>
<labelMode val="2"/>
<lineStyle thickness="4" type="0" typeHidden="2"/>
<arcSize val="40"/>
<selectionAllowed val="false"/>
</element>
<command name="Segment">
<input a0="O" a1="A"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false"/>
<condition showObject="showAngle ∧ select"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-4.12" y="0.93" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="O" a1="B"/>
<output a0="l"/>
</command>
<element type="segment" label="l">
<show object="true" label="false"/>
<condition showObject="showAngle ∧ select"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-4.12" y="0.930000000000001" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="boolean" label="showAngle">
<value val="false"/>
<show object="true" label="true"/>
<condition showObject="select"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelOffset x="15" y="10"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Show angle of rotation"/>
</element>
<expression label="select" exp="a ∨ b ∨ c ∨ d ∨ e ∨ f ∨ g ∨ h ∨ i" />
<element type="boolean" label="select">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="If">
<input a0="e" a1="180°" a2="If[b ∨ c ∨ i, 90°, If[a, 72°, 0°]]"/>
<output a0="matchAngle"/>
</command>
<element type="angle" label="matchAngle">
<angleStyle val="3"/>
<value val="1.2566370614359172"/>
<show object="false" label="true"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
<layer val="3"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
<selectionAllowed val="false"/>
</element>
<expression label="match" exp="Mod[α / °, matchAngle / °] ≟ 0°" />
<element type="boolean" label="match">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="button" label="button0">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="876" y="11"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[lang,If[lang==1,2,1]] RunClickScript[buttonLang]"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="中文"/>
</element>
<element type="button" label="buttonLang">
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="779" y="56"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetCaption[button0,If[lang==1,"ENG","中文"]] SetCaption[a,If[lang==1,"圖案1","Figure 1"]] SetCaption[b,If[lang==1,"圖案2","Figure 2"]] SetCaption[c,If[lang==1,"圖案3","Figure 3"]] SetCaption[d,If[lang==1,"圖案4","Figure 4"]] SetCaption[e,If[lang==1,"圖案5","Figure 5"]] SetCaption[f,If[lang==1,"圖案6","Figure 6"]] SetCaption[g,If[lang==1,"圖案7","Figure 7"]] SetCaption[h,If[lang==1,"圖案8","Figure 8"]] SetCaption[i,If[lang==1,"圖案9","Figure 9"]] SetCaption[showAngle,If[lang==1,"顯示旋轉角度","Show angle of rotation"]]"/>
<font serif="false" sizeM="2" size="20" style="0"/>
</element>
<element type="numeric" label="lang">
<value val="2"/>
<symbolic val="true" />
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="3"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="text1" exp=""" + (If[lang ≟ 1, "旋轉", "Rotate"]) + " " + α + """ />
<element type="text" label="text1">
<show object="true" label="false"/>
<condition showObject="showAngle ∧ select"/>
<objColor r="0" g="0" b="0" alpha="0" dynamicr="If[match, 1, 0.63]" dynamicg="If[match, 0, 0.63]" dynamicb="If[match, 0, 0.63]" colorSpace="0"/>
<layer val="2"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="2" size="20" style="0"/>
<absoluteScreenLocation x="48" y="92"/>
</element>
<expression label="text2" exp=""☟" + (If[lang ≟ 1, "開始", "Start"]) + """ />
<element type="text" label="text2">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-9" y="-12"/>
</element>
<command name="Rotate">
<input a0="pic1" a1="(-α)" a2="O"/>
<output a0="pic1'"/>
</command>
<element type="image" label="pic1'">
<file name="0de44ded35b58b83df1a36bd90cbff85\HKSAR.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.8293421778214047" y="-3.8293421778214034" z="1"/>
<startPoint number="1" x="4.170657822178596" y="-3.8293421778214034" z="1"/>
<startPoint number="2" x="-3.8293421778214047" y="4.123320752295865" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="a"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Rotate">
<input a0="pic2" a1="(-α)" a2="O"/>
<output a0="pic2'"/>
</command>
<element type="image" label="pic2'">
<file name="8af23a4a06fd3b1695f51e838fb94868\Eastern_District_Hong_Kong.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<startPoint number="2" x="-4" y="4.000000209463204" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="b"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Rotate">
<input a0="pic3" a1="(-α)" a2="O"/>
<output a0="pic3'"/>
</command>
<element type="image" label="pic3'">
<file name="59bbf3bcff6ba5f7dd10f7367422d93e\Kwun_Tong_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<startPoint number="2" x="-4" y="3.9619047619047283" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="c"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Rotate">
<input a0="pic4" a1="(-α)" a2="O"/>
<output a0="pic4'"/>
</command>
<element type="image" label="pic4'">
<file name="7165db8fa971a95daa136147e69613bf\Sham_Shui_Po_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.955854104185652" y="-3.9337811562784792" z="1"/>
<startPoint number="1" x="4.0441458958143475" y="-3.9337811562784792" z="1"/>
<startPoint number="2" x="-3.955854104185652" y="3.8757428577213147" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Rotate">
<input a0="pic5" a1="(-α)" a2="O"/>
<output a0="pic5'"/>
</command>
<element type="image" label="pic5'">
<file name="5da28394bd19f4370249b4c67c485964\Shatin_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.9779270520928267" y="-3.889635260464132" z="1"/>
<startPoint number="1" x="4.022072947907173" y="-3.889635260464132" z="1"/>
<startPoint number="2" x="-3.9779270520928267" y="3.9198887535356617" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="e"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Rotate">
<input a0="pic6" a1="(-α)" a2="O"/>
<output a0="pic6'"/>
</command>
<element type="image" label="pic6'">
<file name="dba09a41e755216805c195f4939ed447\Tsuen_Wan_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<startPoint number="2" x="-4" y="4.000000209463204" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Rotate">
<input a0="pic7" a1="(-α)" a2="O"/>
<output a0="pic7'"/>
</command>
<element type="image" label="pic7'">
<file name="c40759008829375adb1ce483627c5cb4\Tuen_Mun_District.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<startPoint number="2" x="-4" y="4.000000209463204" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="g"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Rotate">
<input a0="pic8" a1="(-α)" a2="O"/>
<output a0="pic8'"/>
</command>
<element type="image" label="pic8'">
<file name="87c3484c1e17fc2ac18e64af6161a923\Wong_Tai_Sin District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.9779270520928263" y="-4.088291791628695" z="1"/>
<startPoint number="1" x="4.022072947907174" y="-4.088291791628695" z="1"/>
<startPoint number="2" x="-3.9779270520928263" y="3.9117082083712713" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="h"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Rotate">
<input a0="pic9" a1="(-α)" a2="O"/>
<output a0="pic9'"/>
</command>
<element type="image" label="pic9'">
<file name="7bd025efea0f16552990c8b201bd5119\Yau_Tsim_Mong_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<startPoint number="2" x="-4" y="4.000000209463206" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="i"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
</construction>
</geogebra>