Sum of Exterior Angles of Polygons
2013-02-01 15:44
This GeoGebra applet dynamically demonstrates the geometric theorem that the sum of exterior angles of any convex polygon is always 360°. Users can drag vertices to alter the polygon's shape and number of sides, observing in real time how individual exterior angles change while their sum remains constant. The construction employs the Sequence command to generate vertex lists, along with Polygon an
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<condition showObject="(¬box1) ∧ (n ≥ 6) ∧ showFinger"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="5"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
</element>
<element type="image" label="pic7">
<file name="6a176c013f476cdf4a350d923d832d4b/babc8a566e1acec35744550140d0aa1d\finger_carton_35x45pixels.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="G - (0, (45 * unitPerPixel))"/>
<show object="true" label="false"/>
<condition showObject="(¬box1) ∧ (n ≥ 7) ∧ showFinger"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="5"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
</element>
<element type="image" label="pic8">
<file name="6a176c013f476cdf4a350d923d832d4b/babc8a566e1acec35744550140d0aa1d\finger_carton_35x45pixels.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="H - (0, (45 * unitPerPixel))"/>
<show object="true" label="false"/>
<condition showObject="(¬box1) ∧ (n ≥ 8) ∧ showFinger"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="5"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
</element>
<element type="image" label="pic9">
<file name="6a176c013f476cdf4a350d923d832d4b/babc8a566e1acec35744550140d0aa1d\finger_carton_35x45pixels.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="I - (0, (45 * unitPerPixel))"/>
<show object="true" label="false"/>
<condition showObject="(¬box1) ∧ (n ≥ 9) ∧ showFinger"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="5"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
</element>
<element type="image" label="pic10">
<file name="6a176c013f476cdf4a350d923d832d4b/babc8a566e1acec35744550140d0aa1d\finger_carton_35x45pixels.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="J - (0, (45 * unitPerPixel))"/>
<show object="true" label="false"/>
<condition showObject="(¬box1) ∧ (n ≥ 10) ∧ showFinger"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="5"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
</element>
<element type="boolean" label="showFinger">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="6"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="Circle">
<input a0="(0, 0)" a1="1"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="6"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-1" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Sequence">
<input a0="Ray[listP(i), list2(i)]" a1="i" a2="1" a3="n"/>
<output a0="listRay"/>
</command>
<element type="list" label="listRay">
<show object="true" label="false" ev="4"/>
<condition showObject="box1"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Segment[listP(i), listP(i + 1)]" a1="i" a2="1" a3="n"/>
<output a0="listSeg"/>
</command>
<element type="list" label="listSeg">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<element type="button" label="button0">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="6"/>
<labelOffset x="890" y="21"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<isShape val="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="6"/>
<labelOffset x="976" y="17"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<auxiliary val="true"/>
<ggbscript val="SetCaption[button0,If[lang==1,"ENG","中文"]] SetCaption[listSide,If[lang==1,"邊的數目=","Number of sides="]] SetCaption[box1,If[lang==1,"顯示外角","Show exterior angles"]] SetCaption[box2,If[lang==1,"顯示外角數值","Show angle measures"]] SetCaption[button1,If[lang==1,"放大圖形","Enlarge"]] SetCaption[button2,If[lang==1,"縮小圖形","Reduce"]]"/>
<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"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="6"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="If">
<input a0="simple" a1="If[convex, If[lang ≟ 1, "這是凸多邊形。", "This is a convex polygon."], If[lang ≟ 1, "這是凹多邊形。", "This is a concave polygon."]]" a2="If[lang ≟ 1, "這不是簡單多邊形。", "This is not a simple polygon."]"/>
<output a0="text1"/>
</command>
<element type="text" label="text1">
<show object="true" label="false" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="6"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="2" size="20" style="0"/>
<absoluteScreenLocation x="22" y="103"/>
</element>
</construction>
</geogebra>