Assembling a Triangle: Exploring the Triangle Inequality
2014-06-06 03:49
This GeoGebra applet demonstrates the conditions for forming a triangle. Users select three colored sticks of varying lengths and attempt to assemble them into a triangle, visually exploring the triangle inequality theorem (the sum of any two sides must be greater than the third side). The construction uses geometric objects such as segments, polygons, and circles, combined with commands like Rand
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.4" version="4.4.37.0" id="5dd33940-099c-4002-aeb2-1b405cb1a61f" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="913" height="758" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.4348302300109529" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1" size="400" window="490,85,724,686" />
<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 || 66 68 || 6" visible="false" inframe="false" stylebar="true" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="897" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="397" window="264,135,380,554" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" 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" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" 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="1" help="false" />
<input show="false" cmd="false" top="false" />
<dockBar show="false" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="20"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<size width="897" height="679"/>
<coordSystem xZero="628.4107376483895" yZero="-1411.6000388947216" scale="10.217793421920412" yscale="10.217793421920407"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="1" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="0" g="0" b="0"/>
<axesColor r="255" g="255" b="255"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="2" showNumbers="false"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="2" showNumbers="false"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
<startAnimation val="true"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<expression label ="集合1" exp="{1, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 2, 3, 4, 5, 6, 7, 8, 9, 10}"/>
<element type="list" label="集合1">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label="w_1" exp="(x(Corner[2]) - x(Corner[1])) / 20" />
<element type="numeric" label="w_1">
<value val="4.399188566835573"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="P" exp="(((9 * Corner[1]) + Corner[2]) / 10 + ((6 * Corner[1]) + (4 * Corner[4])) / 10) / 2" type="point" />
<element type="point" label="P">
<show object="false" label="true"/>
<objColor r="255" g="255" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-57.20028909515196" y="-191.37204660056722" z="1.0"/>
<pointSize val="9"/>
<pointStyle val="2"/>
</element>
<expression label="v_1" exp="(y(Corner[4]) - y(Corner[1])) / 20" />
<element type="numeric" label="v_1">
<value val="3.332422040061208"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Segment">
<input a0="Midpoint[Corner[1], Corner[2]]" a1="Midpoint[Corner[3], Corner[4]]"/>
<output a0="p"/>
</command>
<element type="segment" label="p">
<show object="true" label="false"/>
<condition showObject="a_2 ≟ false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-66.64844080122415" y="0.0" z="-1173.5185526396776"/>
<lineStyle thickness="2" type="20" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="y = y(P)" a1="p"/>
<output a0="O"/>
</command>
<element type="point" label="O">
<show object="false" label="false"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="8" y="40"/>
<labelMode val="0"/>
<coords x="-1173.5185526396776" y="-12754.648518867014" z="66.64844080122415"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="O" a1="(12.6 * v_1)"/>
<output a0="c_2"/>
</command>
<element type="conic" label="c_2">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="9"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="35170.25189685999" A3="0.0" A4="17.607591993631804" A5="191.37204660056722"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="c_2" a1="p"/>
<output a0="V" a1=""/>
</command>
<element type="point" label="V">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="9"/>
<labelMode val="0"/>
<coords x="-17.607591993631804" y="-149.383528895796" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="RandomElement">
<input a0="集合1"/>
<output a0="a"/>
</command>
<element type="numeric" label="a">
<value val="7.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<element type="point" label="A">
<show object="true" label="false"/>
<condition showObject="t_1 ≟ false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-57.20028909515196" y="-158.04782619995513" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<command name="RandomElement">
<input a0="集合1"/>
<output a0="c"/>
</command>
<element type="numeric" label="c">
<value val="6.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="RandomElement">
<input a0="集合1"/>
<output a0="d"/>
</command>
<element type="numeric" label="d">
<value val="2.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="RandomElement">
<input a0="集合1"/>
<output a0="e"/>
</command>
<element type="numeric" label="e">
<value val="3.5"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="RandomElement">
<input a0="集合1"/>
<output a0="f"/>
</command>
<element type="numeric" label="f">
<value val="10.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="u_1" exp="floor((x(Corner[2]) - x(Corner[1])) / 22)" />
<element type="numeric" label="u_1">
<value val="3.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="B" exp="A + ((a * u_1), 0)" type="point" />
<element type="point" label="B">
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-36.20028909515196" y="-158.04782619995513" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="true"/>
<condition showObject="t_1 ≟ false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="5"/>
<labelOffset x="-19" y="17"/>
<labelMode val="2"/>
<coords x="0.0" y="21.0" z="3319.0043501990585"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="C">
<show object="false" label="false"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="25" y="2"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-57.20028909515196" y="-151.38298211983272" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="b">
<value val="11.0"/>
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="D" exp="C + ((b * u_1), 0)" type="point" />
<element type="point" label="D">
<show object="false" label="false"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-24.20028909515196" y="-151.38298211983272" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="C" a1="D"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="false" label="true"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="5"/>
<labelOffset x="-7" y="10"/>
<labelMode val="2"/>
<coords x="0.0" y="33.0" z="4995.638409954479"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="E">
<show object="true" label="false"/>
<condition showObject="t_1 ≟ false"/>
<objColor r="255" g="255" b="0" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-57.20028909515196" y="-164.71267028007756" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<expression label="F" exp="E + ((c * u_1), 0)" type="point" />
<element type="point" label="F">
<show object="false" label="false"/>
<objColor r="255" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-39.20028909515196" y="-164.71267028007756" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="E" a1="F"/>
<output a0="k"/>
</command>
<element type="segment" label="k">
<show object="true" label="true"/>
<condition showObject="t_1 ≟ false"/>
<objColor r="255" g="255" b="0" alpha="0.0"/>
<layer val="5"/>
<labelOffset x="-5" y="14"/>
<labelMode val="2"/>
<coords x="0.0" y="18.0" z="2964.8280650413953"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="G">
<show object="true" label="false"/>
<condition showObject="t_1 ≟ false"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-57.20028909515196" y="-171.37751436019997" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<expression label="H" exp="G + ((d * u_1), 0)" type="point" />
<element type="point" label="H">
<show object="false" label="false"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-51.20028909515196" y="-171.37751436019997" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="G" a1="H"/>
<output a0="l"/>
</command>
<element type="segment" label="l">
<show object="true" label="true"/>
<condition showObject="t_1 ≟ false"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="5"/>
<labelOffset x="-8" y="17"/>
<labelMode val="2"/>
<coords x="0.0" y="6.0" z="1028.2650861612"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="I">
<show object="true" label="false"/>
<condition showObject="t_1 ≟ false"/>
<objColor r="0" g="255" b="255" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-57.20028909515196" y="-178.04235844032237" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<expression label="J" exp="I + ((f * u_1), 0)" type="point" />
<element type="point" label="J">
<show object="false" label="false"/>
<objColor r="0" g="255" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-27.20028909515196" y="-178.04235844032237" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="I" a1="J"/>
<output a0="m"/>
</command>
<element type="segment" label="m">
<show object="true" label="true"/>
<condition showObject="t_1 ≟ false"/>
<objColor r="0" g="255" b="255" alpha="0.0"/>
<layer val="5"/>
<labelOffset x="0" y="12"/>
<labelMode val="2"/>
<coords x="0.0" y="30.0" z="5341.270753209671"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="K">
<show object="true" label="false"/>
<condition showObject="t_1 ≟ false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-57.20028909515196" y="-184.7072025204448" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<expression label="L" exp="K + ((e * u_1), 0)" type="point" />
<element type="point" label="L">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-46.70028909515196" y="-184.7072025204448" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="K" a1="L"/>
<output a0="n"/>
</command>
<element type="segment" label="n">
<show object="true" label="true"/>
<condition showObject="t_1 ≟ false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="5"/>
<labelOffset x="-19" y="15"/>
<labelMode val="2"/>
<coords x="0.0" y="10.5" z="1939.4256264646701"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="M">
<show object="true" label="false"/>
<condition showObject="t_1 ≟ false"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-57.20028909515196" y="-191.37204660056722" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<command name="RandomElement">
<input a0="集合1"/>
<output a0="g"/>
</command>
<element type="numeric" label="g">
<value val="7.5"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="N" exp="M + ((g * u_1), 0)" type="point" />
<element type="point" label="N">
<show object="false" label="false"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-34.70028909515196" y="-191.37204660056722" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="M" a1="N"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="true"/>
<condition showObject="t_1 ≟ false"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="5"/>
<labelOffset x="-1" y="14"/>
<labelMode val="2"/>
<coords x="0.0" y="22.5" z="4305.871048512763"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="button" label="按钮1">
<show object="true" label="true"/>
<condition showObject="a_2 ≟ false"/>
<objColor r="255" g="0" b="0" alpha="1.0"/>
<bgColor r="191" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="46" y="101"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="UpdateConstruction[] SetValue[t_1,false] SetValue[A,Element[集合2,6]] SetValue[C,Element[集合2,7]] SetValue[M,Element[集合2,1]] SetValue[E,Element[集合2,5]] SetValue[G,Element[集合2,4]] SetValue[I,Element[集合2,3]] SetValue[K,Element[集合2,2]]"/>
<font serif="false" sizeM="2.0" size="20" style="1"/>
<caption val="换棒"/>
</element>
<command name="Sequence">
<input a0="Translate[P, Vector[(i * Vector[(0, (y(Corner[4]) - y(Corner[1])) / 10)])]]" a1="i" a2="0" a3="6"/>
<output a0="集合2"/>
</command>
<element type="list" label="集合2">
<show object="false" label="false"/>
<objColor r="255" g="255" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="9"/>
<pointStyle val="2"/>
</element>
<expression label="集合3" exp="{A, C, E, I, G, K, M}" />
<element type="list" label="集合3">
<show object="true" label="false"/>
<objColor r="255" g="255" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="If">
<input a0="x(A) > x(O)" a1="a"/>
<output a0="o"/>
</command>
<element type="numeric" label="o">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="x(C) > x(O)" a1="b"/>
<output a0="q"/>
</command>
<element type="numeric" label="q">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="x(E) > x(O)" a1="c"/>
<output a0="r"/>
</command>
<element type="numeric" label="r">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="x(G) > x(O)" a1="d"/>
<output a0="s"/>
</command>
<element type="numeric" label="s">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="x(I) > x(O)" a1="f"/>
<output a0="t"/>
</command>
<element type="numeric" label="t">
<value val="NaN"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
</element>
<command name="If">
<input a0="x(K) > x(O)" a1="e"/>
<output a0="u"/>
</command>
<element type="numeric" label="u">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="x(M) > x(O)" a1="g"/>
<output a0="v"/>
</command>
<element type="numeric" label="v">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="集合4" exp="{o, q, r, s, t, u, v}" />
<element type="list" label="集合4">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="RemoveUndefined">
<input a0="集合4"/>
<output a0="集合5"/>
</command>
<element type="list" label="集合5">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<listType val="numeric"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label="w" exp="(Element[集合5, 1] * u_1)" />
<element type="numeric" label="w">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="a_1" exp="(Element[集合5, 2] * u_1)" />
<element type="numeric" label="a_1">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="b_1" exp="(Element[集合5, 3] * u_1)" />
<element type="numeric" label="b_1">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="Q" exp="O - (w / 2, 0)" type="point" />
<element type="point" label="Q">
<show object="true" label="false"/>
<condition showObject="t_1"/>
<objColor r="255" g="127" b="0" alpha="0.0" dynamicr="k_1" dynamicg="l_1" dynamicb="m_1" colorSpace="0"/>
<layer val="0"/>
<labelOffset x="-39" y="45"/>
<labelMode val="0"/>
<coords x="NaN" y="-191.37204660056722" z="1.0"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<expression label="R" exp="(x(Q) + w, y(Q))" type="point" />
<element type="point" label="R">
<show object="true" label="false"/>
<condition showObject="t_1"/>
<objColor r="255" g="0" b="0" alpha="0.0" dynamicr="n_1" dynamicg="o_1" dynamicb="p_1" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="Q" a1="b_1"/>
<output a0="c_1"/>
</command>
<element type="conic" label="c_1">
<show object="false" label="true"/>
<objColor r="255" g="255" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="NaN" A3="0.0" A4="22.857591993631804" A5="191.37204660056722"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="R" a1="a_1"/>
<output a0="d_1"/>
</command>
<element type="conic" label="d_1">
<show object="false" label="true"/>
<objColor r="255" g="255" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="NaN" A3="0.0" A4="12.357591993631804" A5="191.37204660056722"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="c_1" a1="d_1" a2="1"/>
<output a0="T"/>
</command>
<element type="point" label="T">
<show object="true" label="false"/>
<condition showObject="t_1"/>
<objColor r="255" g="0" b="0" alpha="0.0" dynamicr="q_1" dynamicg="r_1" dynamicb="s_1" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="Q" a1="R"/>
<output a0="e_1"/>
</command>
<element type="segment" label="e_1">
<show object="true" label="false"/>
<condition showObject="t_1"/>
<objColor r="255" g="127" b="0" alpha="0.0" dynamicr="k_1" dynamicg="l_1" dynamicb="m_1" colorSpace="0"/>
<layer val="5"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="R" a1="T"/>
<output a0="f_1"/>
</command>
<element type="segment" label="f_1">
<show object="true" label="false"/>
<condition showObject="t_1"/>
<objColor r="255" g="0" b="0" alpha="0.0" dynamicr="n_1" dynamicg="o_1" dynamicb="p_1" colorSpace="0"/>
<layer val="5"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="T" a1="Q"/>
<output a0="g_1"/>
</command>
<element type="segment" label="g_1">
<show object="true" label="false"/>
<condition showObject="t_1"/>
<objColor r="255" g="0" b="0" alpha="0.0" dynamicr="q_1" dynamicg="r_1" dynamicb="s_1" colorSpace="0"/>
<layer val="5"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="If">
<input a0="w ≟ a" a1="1" a2="If[w ≟ b, 2, If[w ≟ c, 3, If[w ≟ d, 4, If[w ≟ e, 6, If[w ≟ f, 5, If[w ≟ g, 7]]]]]]"/>
<output a0="h_1"/>
</command>
<element type="numeric" label="h_1">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="a_1 ≟ a" a1="1" a2="If[a_1 ≟ b, 2, If[a_1 ≟ c, 3, If[a_1 ≟ d, 4, If[a_1 ≟ e, 6, If[a_1 ≟ f, 5, If[a_1 ≟ g, 7]]]]]]"/>
<output a0="i_1"/>
</command>
<element type="numeric" label="i_1">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="b_1 ≟ a" a1="1" a2="If[b_1 ≟ b, 2, If[b_1 ≟ c, 3, If[b_1 ≟ d, 4, If[b_1 ≟ e, 6, If[b_1 ≟ f, 5, If[b_1 ≟ g, 7]]]]]]"/>
<output a0="j_1"/>
</command>
<element type="numeric" label="j_1">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="h_1 < 4" a1="255" a2="If[h_1 < 7, 0, 255]"/>
<output a0="k_1"/>
</command>
<element type="numeric" label="k_1">
<value val="255.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="h_1 < 2" a1="0" a2="If[h_1 < 3, 127, If[h_1 < 6, 255, If[h_1 < 8, 0]]]"/>
<output a0="l_1"/>
</command>
<element type="numeric" label="l_1">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="h_1 < 5" a1="0" a2="255"/>
<output a0="m_1"/>
</command>
<element type="numeric" label="m_1">
<value val="255.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="i_1 < 4" a1="255" a2="If[i_1 < 7, 0, 255]"/>
<output a0="n_1"/>
</command>
<element type="numeric" label="n_1">
<value val="255.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="i_1 < 2" a1="0" a2="If[i_1 < 6, 255, If[i_1 < 8, 0]]"/>
<output a0="o_1"/>
</command>
<element type="numeric" label="o_1">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="i_1 < 5" a1="0" a2="255"/>
<output a0="p_1"/>
</command>
<element type="numeric" label="p_1">
<value val="255.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="j_1 < 4" a1="255" a2="If[j_1 < 7, 0, 255]"/>
<output a0="q_1"/>
</command>
<element type="numeric" label="q_1">
<value val="255.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="j_1 < 2" a1="0" a2="If[j_1 < 3, 127, If[j_1 < 6, 255, If[j_1 < 8, 0]]]"/>
<output a0="r_1"/>
</command>
<element type="numeric" label="r_1">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="j_1 < 5" a1="0" a2="255"/>
<output a0="s_1"/>
</command>
<element type="numeric" label="s_1">
<value val="255.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<element type="button" label="按钮2">
<show object="true" label="true"/>
<condition showObject="a_2 ≟ false"/>
<objColor r="191" g="255" b="0" alpha="1.0"/>
<bgColor r="255" g="0" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="120" y="101"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t_1,If[t_1,false,true]]"/>
<font serif="false" sizeM="2.0" size="20" style="1"/>
<caption val="组合"/>
</element>
<element type="boolean" label="t_1">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="511" y="138"/>
<labelMode val="0"/>
</element>
<command name="Polygon">
<input a0="T" a1="Q" a2="R"/>
<output a0="多边形1" a1="r_2" a2="t_2" a3="q_2"/>
</command>
<element type="polygon" label="多边形1">
<lineStyle thickness="2" type="10" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="t_1"/>
<objColor r="125" g="125" b="255" alpha="1.0" dynamicr="n_2" dynamicg="i_2" dynamicb="j_2" dynamica="1" colorSpace="0" fillType="3" hatchAngle="45" hatchDistance="5"/>
<layer val="1"/>
<labelMode val="0"/>
</element>
<element type="segment" label="r_2">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="10" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="t_2">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="10" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="q_2">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="10" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="numeric" label="n_2">
<value val="50.0" random="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="5"/>
<labelOffset x="55" y="0"/>
<labelMode val="1"/>
<slider min="1" max="255" absoluteScreenLocation="true" width="200.0" x="-16.0" y="88.0" fixed="true" horizontal="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="0.05" type="0" playing="true"/>
</element>
<element type="numeric" label="i_2">
<value val="144.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="5"/>
<labelOffset x="42" y="26"/>
<labelMode val="1"/>
<slider min="1" max="255" absoluteScreenLocation="true" width="200.0" x="15.0" y="31.0" fixed="true" horizontal="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="0.05" type="0" playing="true"/>
</element>
<element type="numeric" label="j_2">
<value val="141.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="5"/>
<labelMode val="1"/>
<slider min="1" max="255" absoluteScreenLocation="true" width="200.0" x="235.0" y="101.0" fixed="true" horizontal="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="0.05" type="0" playing="true"/>
</element>
<element type="image" label="图1">
<file name="de3d3e3412512d0a7946d87ee97f67a3\transferImage.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="W"/>
<startPoint number="1" exp="Z"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="9"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
</element>
<command name="Circle">
<input a0="V" a1="(5 * w_1)"/>
<output a0="d_2"/>
</command>
<element type="conic" label="d_2">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="9"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="22141.644500010905" A3="0.0" A4="17.607591993631804" A5="149.383528895796"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="c_2" a1="d_2"/>
<output a0="W" a1="Z" a2="" a3=""/>
</command>
<element type="point" label="W">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="9"/>
<labelMode val="0"/>
<coords x="-38.8355992324354" y="-155.1448837567398" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="Z">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="9"/>
<labelMode val="0"/>
<coords x="3.620415245171788" y="-155.1448837567398" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Midpoint">
<input a0="P" a1="O"/>
<output a0="S"/>
</command>
<element type="point" label="S">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="9"/>
<labelMode val="0"/>
<coords x="-37.40394054439188" y="-191.37204660056722" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="image" label="图2">
<file name="aba35d7a6832ee78023c8c00705d3af9\transferImage.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="S"/>
<startPoint number="1" exp="U"/>
<show object="true" label="false"/>
<condition showObject="a_2"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
</element>
<element type="image" label="图3">
<file name="c8afd29ba4674bc80f34d950aeb1b8ab\transferImage.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="A_1"/>
<startPoint number="1" exp="B_1"/>
<show object="true" label="false"/>
<condition showObject="a_2"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
</element>
<expression label="B_1" exp="S + (w_1 / 4, 0)" type="point" />
<element type="point" label="B_1">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="9"/>
<labelMode val="0"/>
<coords x="-36.30414340268299" y="-191.37204660056722" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="U" exp="S + ((13 * w_1), 0)" type="point" />
<element type="point" label="U">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="9"/>
<labelMode val="0"/>
<coords x="19.78551082447057" y="-191.37204660056722" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="A_1" exp="S - ((4 * w_1), 0)" type="point" />
<element type="point" label="A_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="9"/>
<labelMode val="0"/>
<coords x="-55.00069481173417" y="-191.37204660056722" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="boolean" label="a_2">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="9"/>
<labelOffset x="514" y="129"/>
<labelMode val="0"/>
<ggbscript onUpdate="SetValue[t_1,false]"/>
</element>
<element type="button" label="按钮3">
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="1.0"/>
<bgColor r="0" g="255" b="255" alpha="255"/>
<layer val="9"/>
<labelOffset x="48" y="45"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[a_2,If[a_2,false,true]] SetValue[t_1,If[t_1,false,true]]"/>
<font serif="false" sizeM="2.0" size="20" style="1"/>
<caption val="怎么玩？"/>
</element>
</construction>
</geogebra>