Circles of Equal Size
2019-07-25 01:36
This applet demonstrates how to construct a sequence of circles of equal size using the Sequence and Translate commands in GeoGebra. By defining an initial circle and a translation vector, it visually illustrates the geometric properties of circles, translation transformations, and the efficient application of sequences in geometric constructions.
In collections
The Beauty of Mathematics | GeoGebra Book
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.550.0" app="classic" platform="w" id="3AB69398-3C8D-43B0-8EBC-7F1657308779" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1440" height="742" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.25555555555555554" orientation="1" />
</panes>
<views>
<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 | 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 || 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="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 | 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="428" window="100,100,700,550" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1064" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="368" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="300" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="300" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="480" 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="900" 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="true" items="0 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="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1064" height="646"/>
<coordSystem xZero="456.20791528630906" yZero="326.32884834941245" scale="12.9365305024009" yscale="12.936530502400872"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" 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="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="3"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="3" spreadsheet="0"/>
<coordStyle val="0"/>
<startAnimation val="true"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="大小相等的圆" author="" date="">
<element type="numeric" label="rl">
<value val="0.5"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="200" x="30" y="50" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.2" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="rr">
<value val="2"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="5" absoluteScreenLocation="true" width="200" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="d">
<value val="8"/>
<symbolic val="true" />
<show object="false" label="true"/>
<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" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="OL" exp="((-d), 0)" type="point" />
<element type="point" label="OL">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-8" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="OR" exp="(d, 0)" type="point" />
<element type="point" label="OR">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="8" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="OL" a1="1"/>
<output a0="CL"/>
</command>
<element type="conic" label="CL">
<show object="true" label="false"/>
<objColor r="204" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" 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="63" A3="0" A4="8" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="OR" a1="1"/>
<output a0="CR"/>
</command>
<element type="conic" label="CR">
<show object="true" label="false"/>
<objColor r="204" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" 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="63" A3="0" A4="-8" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="OL + (1 + (1.5 * rl), 0)" a1="rl"/>
<output a0="CL0"/>
</command>
<element type="conic" label="CL0">
<show object="false" label="false"/>
<objColor r="102" g="204" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="0" y="33"/>
<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="38.8125" A3="0" A4="6.25" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="OR + (0.2 + (2 * rr), 0)" a1="rr"/>
<output a0="CR0"/>
</command>
<element type="conic" label="CR0">
<show object="false" 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="144.83999999999997" A3="0" A4="-12.2" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Sequence">
<input a0="Rotate[CR0, (π / 3 * k), OR]" a1="k" a2="1" a3="6"/>
<output a0="l1"/>
</command>
<element type="list" label="l1">
<show object="true" label="true"/>
<objColor r="102" g="204" b="255" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<element type="numeric" label="t">
<value val="0.89"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="200" x="30" y="50" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.01" speed="1" type="0" playing="true"/>
</element>
<command name="Translate">
<input a0="CL" a1="Vector[(t * Vector[OL, OR])]"/>
<output a0="Cs"/>
</command>
<element type="conic" label="Cs">
<show object="true" label="false"/>
<objColor r="204" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" 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="37.9376" A3="0" A4="-6.24" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Sequence">
<input a0="Rotate[CL0, (π / 3 * k), OL]" a1="k" a2="1" a3="8"/>
<output a0="CLs"/>
</command>
<element type="list" label="CLs">
<show object="true" label="true"/>
<objColor r="102" g="204" b="255" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
</construction>
</geogebra>