Colorful Circle: Circular Pattern Construction via Sequence and Reflection
2020-07-19 11:15
This GeoGebra example demonstrates how to construct a visually striking circular pattern using the Circle, Sequence, and Mirror commands. By defining a base circle and key points, the Sequence command generates multiple geometric objects in bulk, and the Mirror command applies reflective symmetry to produce a colorful, kaleidoscopic circular design. It is ideal for exploring circle symmetry, batch
In collections
Minority Pi GeoGebra Collection
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.593.0" app="classic" platform="d" id="cea3f132-3a4c-4cf3-9879-a8d976a84faa" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1366" height="728" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.7833089311859444" orientation="1" />
<pane location="0" divider="0.2020497803806735" 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="true" location="3,1,1" size="372" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="3,1" size="789" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="true" location="3,3" size="276" 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="16" visible="false" inframe="false" stylebar="true" location="3,1" size="544" 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 51 | 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 , 538 | 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" size="520" window="100,100,600,400" />
<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="false" location="1" size="150" window="50,50,500,500" />
<view id="4097" visible="true" inframe="false" stylebar="true" location="1" size="264" window="100,100,700,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" 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="true" cmd="true" top="true" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="18"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="789" height="497"/>
<coordSystem xZero="338.35465185365763" yZero="252.72693654171246" scale="32.80344921493338" yscale="32.80344921493336"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="0" g="51" b="0"/>
<axesColor r="255" g="255" b="255"/>
<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>
<algebraView>
<mode val="1"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2.0" max="2.0" step="1.0"/>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="0.0" yZero="0.0" zZero="-1.5" scale="50.0" xAngle="20.0" zAngle="-60.0"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="3"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="2" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<plate show="true"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="1"/>
<projection type="0"/>
</euclidianView3D>
<construction title="" author="" date="">
<expression label="A" exp="(0, 0)" type="point"/>
<element type="point" label="A">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<coords x="0.0" y="0.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="(0, 0)" a1="5"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<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="-25.0" A3="0.0" A4="-0.0" A5="-0.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-34" y="11"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<coords x="-4.946471064742007" y="0.7296739036515363" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="n">
<value val="1.0"/>
<show object="true" label="true"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="30" width="4.0" x="-6.943112371330807" y="5.935777183150158" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="true"/>
<ggbscript onUpdate=""/>
</element>
<command name="Sequence">
<input a0="Semicircle[A, Rotate[B, (360° * k / n), A]]" a1="k" a2="1" a3="n"/>
<output a0="l1"/>
</command>
<element type="list" label="l1">
<show object="true" label="false" ev="4"/>
<objColor r="214" g="58" b="108" alpha="0.0" dynamicr="(2 * x(B))" dynamicg="(3 * y(B))" dynamicb="(5 * x(B))" dynamica="0" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<trace val="true"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Mirror">
<input a0="B" a1="A"/>
<output a0="B'"/>
</command>
<element type="point" label="B'">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<coords x="4.946471064742007" y="-0.7296739036515363" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Semicircle[A, Rotate[B', (360° * k / n), A]]" a1="k" a2="1" a3="n"/>
<output a0="l2"/>
</command>
<element type="list" label="l2">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0" dynamicr="x(B')" dynamicg="(3 * y(B'))" dynamicb="(6 * x(B'))" dynamica="0" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<trace val="true"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Semicircle[A, Rotate[B', (360° * k / n), A]]" a1="k" a2="1" a3="n"/>
<output a0="l3"/>
</command>
<element type="list" label="l3">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="false" label="true" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-0.04062352401393541" y="4.9998349702061855" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="false" label="true" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0.2627759012961477" y="-4.9930901079089285" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Semicircle[A, Rotate[C, (360° * k / n), A]]" a1="k" a2="1" a3="n"/>
<output a0="l4"/>
</command>
<element type="list" label="l4">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<trace val="true"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Semicircle[A, Rotate[D, (360° * k / n), A]]" a1="k" a2="1" a3="n"/>
<output a0="l5"/>
</command>
<element type="list" label="l5">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<trace val="true"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
</construction>
</geogebra>