Circle Division Construction Tool
2019-10-16 06:08
This GeoGebra applet demonstrates how to divide a circle into equal parts using geometric construction tools. By utilizing commands such as Intersect, Circle, Segment, and Sequence, it dynamically illustrates the construction process. This tool is ideal for exploring the geometric relationships between regular polygons and circles, helping to intuitively understand the principles of circle divisio
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.562.0" app="classic" platform="w" id="63777460-2937-4ed2-a5c7-07c7d7dffd94" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="923" height="536" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.7269772481040087" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1,1,1" size="400" window="374,254,1468,550" />
<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="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<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="1,1" size="300" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3,3" size="249" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="false" location="3" size="671" window="100,100,600,400" />
<view id="16" visible="true" inframe="false" stylebar="false" location="1" size="242" 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="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" 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" />
</views>
<toolbar show="false" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 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 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="2"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="670" height="533"/>
<coordSystem xZero="318.37222002721484" yZero="260.302193899379" scale="34.03465685575137" yscale="34.03465685575128"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<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="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="241" height="533"/>
<coordSystem xZero="389.2633234192896" yZero="473.8813994409451" scale="30.393834166590906" yscale="30.39383416659092"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<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="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="a">
<value val="6.1"/>
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="10" absoluteScreenLocation="true" width="200" x="15" y="40" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="b">
<value val="5.6"/>
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="a" absoluteScreenLocation="true" width="200" x="15" y="152" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="n">
<value val="60"/>
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="60" absoluteScreenLocation="true" width="200" x="15" y="94" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Intersect">
<input a0="xAxis" a1="yAxis"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="false" ev="4"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="0" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="A" a1="a"/>
<output a0="c_1"/>
</command>
<element type="conic" label="c_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-37.209999999999994" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<expression label="B" exp="((-(a + 0.4)), a + 0.4)" type="point" />
<element type="point" label="B">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-6.5" y="6.5" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="C" exp="(a + 0.4, a + 0.4)" type="point" />
<element type="point" label="C">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="6.5" y="6.5" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="D" exp="(a + 0.4, (-a) - 0.4)" type="point" />
<element type="point" label="D">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="6.5" y="-6.5" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="E" exp="((-a) - 0.4, (-a) - 0.4)" type="point" />
<element type="point" label="E">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-6.5" y="-6.5" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="B" a1="E"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="13" y="0" z="84.5"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="E" a1="D"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="13" z="84.5"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="D" a1="C"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-13" y="0" z="84.5"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="B"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="-13" z="84.5"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="numeric" label="m">
<value val="12"/>
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="60" absoluteScreenLocation="true" width="200" x="15" y="225" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="c">
<value val="5.2"/>
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="b" absoluteScreenLocation="true" width="200" x="18" y="287" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
</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="14" y="412"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="第一刻度虛線"/>
</element>
<element type="boolean" label="e">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="16" y="376"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="圓心"/>
</element>
<expression label="text2" exp=""第一刻度線長度" + (LaTeX[a - b]) + """ />
<element type="text" label="text2">
<show object="true" label="false" ev="43"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="0.75" size="-5" style="0"/>
<absoluteScreenLocation x="11" y="120"/>
</element>
<expression label="text3" exp=""第二刻度線長度" + (LaTeX[a - c]) + """ />
<element type="text" label="text3">
<show object="true" label="false" ev="43"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="0.75" size="-5" style="0"/>
<absoluteScreenLocation x="17" y="254"/>
</element>
<expression label="text1" exp=""圓的半徑" + (LaTeX[a]) + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="43"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="0.75" size="-5" style="0"/>
<absoluteScreenLocation x="10" y="13"/>
</element>
<expression label="text4" exp=""第一刻度線個數" + (LaTeX[n]) + """ />
<element type="text" label="text4">
<show object="true" label="false" ev="43"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="0.75" size="-5" style="0"/>
<absoluteScreenLocation x="11" y="64"/>
</element>
<expression label="text5" exp=""第二刻度線個數 " + (LaTeX[m]) + """ />
<element type="text" label="text5">
<show object="true" label="false" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="0.75" size="-5" style="0"/>
<absoluteScreenLocation x="13" y="190"/>
</element>
<element type="boolean" label="j">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="16" y="453"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="第二刻度虛線"/>
</element>
<element type="angle" label="α">
<angleStyle val="3"/>
<value val="1.5707963267948966"/>
<slider min="0" max="355°" absoluteScreenLocation="true" width="180" x="16" y="338" fixed="false" horizontal="true" showAlgebra="true"/>
<show object="true" label="false" ev="11"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="-1" y="4"/>
<labelMode val="1"/>
<lineStyle thickness="10" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
<animation step="5°" speed="1" type="0" playing="false"/>
</element>
<command name="Sequence">
<input a0="Segment[((a * cos(((2 * π / n) * k) + α)), (a * sin(((2 * π / n) * k) + α))), ((b * cos(((2 * π / n) * k) + α)), (b * sin(((2 * π / n) * k) + α)))]" a1="k" a2="0" a3="n - 1"/>
<output a0="l1"/>
</command>
<element type="list" label="l1">
<show object="true" label="false"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Segment[(0, 0), ((b * cos(((2 * π / n) * k) + α)), (b * sin(((2 * π / n) * k) + α)))]" a1="k" a2="0" a3="n - 1"/>
<output a0="l2"/>
</command>
<element type="list" label="l2">
<show object="false" label="false" ev="4"/>
<condition showObject="d ≠ 0"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="10" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Segment[((a * cos(((2 * π / m) * k) + α)), (a * sin(((2 * π / m) * k) + α))), ((c * cos(((2 * π / m) * k) + α)), (c * sin(((2 * π / m) * k) + α)))]" a1="k" a2="0" a3="m - 1"/>
<output a0="l4"/>
</command>
<element type="list" label="l4">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Segment[(0, 0), ((c * cos(((2 * π / m) * k) + α)), (c * sin(((2 * π / m) * k) + α)))]" a1="k" a2="0" a3="m - 1"/>
<output a0="l5"/>
</command>
<element type="list" label="l5">
<show object="true" label="false" ev="4"/>
<condition showObject="j ≠ 0"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="10" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<expression label="text6" exp=""偏轉角度" + (LaTeX[α]) + """ />
<element type="text" label="text6">
<show object="true" label="false" ev="43"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="0.7" size="-6" style="0"/>
<absoluteScreenLocation x="17" y="301"/>
</element>
</construction>
</geogebra>