整数除法的几何可视化模型演示
2014-04-22 07:12
本GeoGebra范例通过多边形（如梯形）和序列工具，直观演示整数除法及其余数（Mod）的几何意义。将抽象的算术运算转化为可视化的几何分割模型，动态展示被除数、除数、商与余数之间的数量关系。适用于中小学数学教学，帮助学生深入理解整数除法的算理与几何分布特征。
所属专题
五下_分数除法( 教师版)
GeoGebra 画板及绘图内容加载中，请稍等……
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.2" version="4.2.27.0" id="b61b12cd-58de-4928-a2c3-775aa7ede31f" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="988" height="740" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.18218623481781376" orientation="1" />
</panes>
<views>
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,0" size="400" window="747,253,364,423" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="970" window="558,188,465,548" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="180" window="100,100,250,400" />
<view id="8" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="255" window="497,141,588,675" />
<view id="32" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" visible="false" inframe="true" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="4097" visible="false" inframe="true" stylebar="true" location="1" size="150" window="390,238,500,500" />
<view id="70" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" 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 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6" position="1" help="true" />
<input show="false" cmd="true" top="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="2"/>
<font size="18"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<size width="970" height="588"/>
<coordSystem xZero="149.60000000000014" yZero="238.40000000000012" scale="54.99999999999998" yscale="55.0"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="2" rightAngleStyle="1" checkboxSize="13" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<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="1.0" distY="0.1" distTheta="0.5235987755982988"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="a">
<value val="3.0"/>
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="12" absoluteScreenLocation="true" width="120.0" x="12.0" y="112.0" fixed="true" horizontal="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="b">
<value val="5.0"/>
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="5" absoluteScreenLocation="true" width="50.0" x="12.0" y="222.0" fixed="false" horizontal="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Sequence">
<input a0="Segment[(i, 2), (i, 3)]" a1="i" a2="1" a3="a - 1"/>
<output a0="list1"/>
</command>
<element type="list" label="list1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Polygon">
<input a0="(0, 2)" a1="(a, 2)" a2="(a, 3)" a3="(0, 3)"/>
<output a0="poly1" a1="poly1_1" a2="poly1_2" a3="poly1_3" a4="poly1_4"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="7" type="0" typeHidden="1"/>
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
</element>
<element type="segment" label="poly1_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="3.0" z="-6.0"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="poly1_2">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0" y="0.0" z="3.0"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="poly1_3">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-3.0" z="9.0"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="poly1_4">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0" y="0.0" z="0.0"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="Segment[(0, 0), (0, 1)]"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="false" label="false"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.0" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Segment[(b, y(A)), (a, y(A))]"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="5.0" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="A" a1="B" a2="B + (0, 1)" a3="A + (0, 1)"/>
<output a0="poly2" a1="a_1" a2="b_1" a3="c" a4="d"/>
</command>
<element type="polygon" label="poly2">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="a_1">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="5.0" z="0.0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b_1">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0" y="0.0" z="5.0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-5.0" z="5.0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0" y="0.0" z="0.0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Sequence">
<input a0="Polygon[((i - 1) * b, y(A)), (i * b, y(A)), (i * b, y(A) + 1), ((i - 1) * b, y(A) + 1)]" a1="i" a2="1" a3="ceil(x(B) / b)"/>
<output a0="list2"/>
</command>
<element type="list" label="list2">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Sequence[Segment[((j - 1) * b + i, y(A)), ((j - 1) * b + i, y(A) + 1)], i, 1, b - 1]" a1="j" a2="1" a3="ceil(x(B) / b)"/>
<output a0="list3"/>
</command>
<element type="list" label="list3">
<show object="true" label="false"/>
<condition showObject="i"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="3" type="10" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label="text3" exp=""" + b + " 格長紙條"" />
<element type="text" label="text3">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<absoluteScreenLocation x="18" y="207"/>
</element>
<expression label="text2" exp=""" + a + " 個方格"" />
<element type="text" label="text2">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<absoluteScreenLocation x="18" y="97"/>
</element>
<expression label="text4" exp=""→""/>
<element type="text" label="text4">
<show object="true" label="false"/>
<condition showObject="x(B) < a"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<startPoint exp="B"/>
<labelOffset x="2" y="14"/>
</element>
<expression label="text5" exp=""←""/>
<element type="text" label="text5">
<show object="true" label="false"/>
<condition showObject="x(B) > a"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<startPoint exp="B"/>
<labelOffset x="-23" y="13"/>
</element>
<expression label="text7" exp=""" + (LaTeX[floor(x(B) / b)]) + "\;張"" />
<element type="text" label="text7">
<show object="true" label="false"/>
<condition showObject="floor(x(B)) - floor(x(B) / b) * b ≟ 0 ∧ e"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="0"/>
<startPoint exp="B"/>
<labelOffset x="-12" y="24"/>
</element>
<element type="boolean" label="e">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelOffset x="13" y="266"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="紙條數目"/>
</element>
<expression label="text1" exp=""\scalebox{0.7}{" + (LaTeX[a]) + "\;個方格需要多少張\;" + (LaTeX[b]) + "\;格長紙條才能鋪滿？}"" />
<element type="text" label="text1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.8888888888888888" size="16" style="0"/>
<absoluteScreenLocation x="16" y="3"/>
</element>
<command name="Mod">
<input a0="13" a1="4"/>
<output a0="t"/>
</command>
<element type="numeric" label="t">
<value val="1.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<element type="numeric" label="f">
<value val="0.7"/>
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="1"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="text8" exp=""\scalebox{" + (LaTeX[f]) + "}{需要紙：}"" />
<element type="text" label="text8">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.8888888888888888" size="16" style="0"/>
<absoluteScreenLocation x="173" y="309"/>
</element>
<expression label="text9" exp=""\scalebox{" + (LaTeX[f]) + "}{" + (LaTeX[a]) + " ÷ " + (LaTeX[b]) + "}"" />
<element type="text" label="text9">
<show object="true" label="false"/>
<condition showObject="g"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.8888888888888888" size="16" style="0"/>
<absoluteScreenLocation x="383" y="310"/>
</element>
<expression label="text10" exp=""\scalebox{" + (LaTeX[f]) + "}{=\;\frac{" + (LaTeX[a]) + "}{" + (LaTeX[b]) + "}}"" />
<element type="text" label="text10">
<show object="true" label="false"/>
<condition showObject="g ∧ h ∧ ((GCD[a, b] > 1) ∨ (a > b))"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.8888888888888888" size="16" style="0"/>
<absoluteScreenLocation x="348" y="365"/>
</element>
<expression label="text12" exp=""\scalebox{" + (LaTeX[f]) + "}{=\;" + (LaTeX[floor(a / b)]) + "\frac{" + (LaTeX[Mod[a, b]]) + "}{" + (LaTeX[b]) + "}\;（張）}"" />
<element type="text" label="text12">
<show object="true" label="false"/>
<condition showObject="GCD[a, b] ≟ 1 ∧ (a > b) ∧ (Mod[a, b] > 0) ∧ g ∧ h ∧ j"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.8888888888888888" size="16" style="0"/>
<absoluteScreenLocation x="348" y="437"/>
</element>
<expression label="text11" exp=""\scalebox{" + (LaTeX[f]) + "}{=\;" + (LaTeX[floor(a / b)]) + "\frac{" + (LaTeX[Mod[a, b] / GCD[a, b]]) + "}{" + (LaTeX[b / GCD[a, b]]) + "}\;（張）}"" />
<element type="text" label="text11">
<show object="true" label="false"/>
<condition showObject="(GCD[a, b] > 1) ∧ (a > b) ∧ (Mod[a, b] > 0) ∧ g ∧ h ∧ j ∧ k"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.8888888888888888" size="16" style="0"/>
<absoluteScreenLocation x="348" y="513"/>
</element>
<expression label="text12_1" exp=""\scalebox{" + (LaTeX[f]) + "}{=\;" + (LaTeX[floor(a / b)]) + "\frac{" + (LaTeX[Mod[a, b]]) + "}{" + (LaTeX[b]) + "}}"" />
<element type="text" label="text12_1">
<show object="true" label="false"/>
<condition showObject="(GCD[a, b] > 1) ∧ (a > b) ∧ (Mod[a, b] > 0) ∧ g ∧ h ∧ j"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.8888888888888888" size="16" style="0"/>
<absoluteScreenLocation x="348" y="437"/>
</element>
<expression label="text12_2" exp=""\scalebox{" + (LaTeX[f]) + "}{=\;" + (LaTeX[floor(a / b)]) + "\;（張）}"" />
<element type="text" label="text12_2">
<show object="true" label="false"/>
<condition showObject="Mod[a, b] ≟ 0 ∧ g ∧ h ∧ j"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.8888888888888888" size="16" style="0"/>
<absoluteScreenLocation x="348" y="437"/>
</element>
<expression label="text10_1" exp=""\scalebox{" + (LaTeX[f]) + "}{=\;\frac{" + (LaTeX[a]) + "}{" + (LaTeX[b]) + "}\;（張）}"" />
<element type="text" label="text10_1">
<show object="true" label="false"/>
<condition showObject="(a < b) ∧ GCD[a, b] ≟ 1 ∧ g ∧ h"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.8888888888888888" size="16" style="0"/>
<absoluteScreenLocation x="348" y="365"/>
</element>
<expression label="text12_3" exp=""\scalebox{" + (LaTeX[f]) + "}{=\;\frac{" + (LaTeX[a / GCD[a, b]]) + "}{" + (LaTeX[b / GCD[a, b]]) + "}\;（張）}"" />
<element type="text" label="text12_3">
<show object="true" label="false"/>
<condition showObject="(a < b) ∧ (GCD[a, b] > 1) ∧ g ∧ h ∧ j"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.8888888888888888" size="16" style="0"/>
<absoluteScreenLocation x="348" y="437"/>
</element>
<element type="boolean" label="g">
<value val="false"/>
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelOffset x="519" y="327"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="boolean" label="h">
<value val="false"/>
<show object="true" label="false"/>
<condition showObject="g"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelOffset x="519" y="387"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="text6" exp=""" + (LaTeX[floor(x(B) / b)]) + "\frac{" + (LaTeX[floor(x(B)) - floor(x(B) / b) * b]) + "}{" + (LaTeX[b]) + "}\;張"" />
<element type="text" label="text6">
<show object="true" label="false"/>
<condition showObject="(floor(x(B)) - floor(x(B) / b) * b ≠ 0) ∧ (a > b) ∧ e"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="0"/>
<startPoint exp="B"/>
<labelOffset x="-13" y="12"/>
</element>
<element type="numeric" label="B1">
<value val="0.0"/>
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="1"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
</element>
<expression label="text6_1" exp=""\frac{" + (LaTeX[floor(x(B)) - floor(x(B) / b) * b]) + "}{" + (LaTeX[b]) + "}\;張"" />
<element type="text" label="text6_1">
<show object="true" label="false"/>
<condition showObject="(floor(x(B)) - floor(x(B) / b) * b ≠ 0) ∧ (a < b) ∧ e"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="0"/>
<startPoint exp="B"/>
<labelOffset x="-13" y="12"/>
</element>
<element type="boolean" label="i">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelOffset x="145" y="250"/>
<labelMode val="0"/>
<caption val="格線"/>
</element>
<element type="boolean" label="j">
<value val="false"/>
<show object="true" label="false"/>
<condition showObject="g ∧ h ∧ ((a ≥ b) ∨ (GCD[a, b] > 1))"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelOffset x="519" y="459"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="boolean" label="k">
<value val="false"/>
<show object="true" label="false"/>
<condition showObject="g ∧ h ∧ j ∧ (a > b) ∧ (GCD[a, b] > 1) ∧ (Mod[a, b] > 0)"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelOffset x="519" y="536"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
</construction>
</geogebra>