几何圆构造演示
2015-12-27 03:07
本 GeoGebra 范例演示了几何圆的构造过程。通过 Sequence 和 If 等命令生成一系列几何对象，包括圆心、半径、列表序列等元素，结合按钮交互实现动态作图。范例涉及圆的基本几何性质，展示了如何利用序列命令批量生成与圆相关的几何元素，适合用于几何作图教学与圆的性质探究。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.189.0" id="56ceea64-8c62-4e00-8072-edbfc6fece86" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="848" height="711" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.2759433962264151" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1" size="400" window="108,457,1289,550" />
<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="false" 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 || 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="true" location="1" size="580" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="true" location="3" size="234" window="100,100,250,400" />
<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" toolbar="0" 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" />
<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" size="300" 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 73 , 14 66 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="false" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="580" height="456"/>
<coordSystem xZero="259.72331934998937" yZero="213.76987017274902" scale="32.219304744990566" yscale="32.219294657555764"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="1" rightAngleStyle="1" checkboxSize="13" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="96" g="96" b="96"/>
<lineStyle axes="15" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="false" tickDistance="0.5"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="false" tickDistance="0.5"/>
<grid distX="1.0" distY="1.0" 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="Geometric Circle" author="" date="">
<element type="boolean" label="mix">
<value val="true"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="34" y="62"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="angle" label="th">
<angleStyle val="3"/>
<value val="0.0"/>
<slider min="0" max="360°" absoluteScreenLocation="true" width="180.0" x="39.0" y="34.0" fixed="true" horizontal="true" showAlgebra="true"/>
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="10" type="0" typeHidden="2"/>
<arcSize val="30"/>
<animation step="0.017453292519943295" speed="5" type="1" playing="true"/>
</element>
<expression label ="O" exp="O:(0, 0)" type="point"/>
<element type="point" label="O">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-25" y="6"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0.0" y="0.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="n">
<value val="11.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="20" absoluteScreenLocation="true" width="200.0" x="30.0" y="90.0" fixed="false" horizontal="true" showAlgebra="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Sequence">
<input a0="CircleArc[(2; th - 60° + (30° * i)), (2; th + (30° * i)), O]" a1="i" a2="0" a3="n"/>
<output a0="list1"/>
</command>
<element type="list" label="list1">
<show object="true" label="false" ev="4"/>
<objColor r="102" g="51" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="9" type="-1" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<element type="angle" label="rth">
<angleStyle val="3"/>
<value val="1.0471975511965976"/>
<slider min="0°" max="6.283185307179586" absoluteScreenLocation="true" width="180.0" x="297.0" y="34.0" fixed="true" horizontal="true" showAlgebra="false"/>
<show object="true" label="true" ev="4"/>
<objColor r="51" g="51" b="255" alpha="0.9"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
<animation step="15°" speed="1" type="0" playing="false"/>
</element>
<command name="Sequence">
<input a0="Segment[(2; th + (30° * i)), (2; th + (30° * i)) + (2; th + (30° * i) + rth)]" a1="i" a2="0" a3="n"/>
<output a0="list2"/>
</command>
<element type="list" label="list2">
<show object="true" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="9" type="-1" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<expression label="r1" exp="(4 * cos(rth / 2))" />
<element type="numeric" label="r1">
<value val="3.464101615137755"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="or1" exp="(r1 * cos(rth / 2 + 15°))" />
<element type="numeric" label="or1">
<value val="2.4494897427831783"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="hr1" exp="(r1 * sin(rth / 2 + 15°))" />
<element type="numeric" label="hr1">
<value val="2.449489742783178"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="mix" a1="(-th)" a2="0°"/>
<output a0="nth"/>
</command>
<element type="angle" label="nth">
<angleStyle val="3"/>
<value val="-0.0"/>
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
</element>
<command name="Sequence">
<input a0="CircleArc[(or1; th + (30° * i) - 15°), (or1 + hr1; th + (30° * i) - 15°), (r1; th + (30° * i) + rth / 2)]" a1="i" a2="0" a3="n"/>
<output a0="list3"/>
</command>
<element type="list" label="list3">
<show object="true" label="false" ev="4"/>
<objColor r="204" g="153" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="9" type="-1" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="CircleArc[(2; nth + 60° + (30° * i)), O, (2; nth + (30° * i))]" a1="i" a2="0" a3="n"/>
<output a0="list4"/>
</command>
<element type="list" label="list4">
<show object="true" label="false" ev="4"/>
<objColor r="102" g="51" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="9" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Segment[(2; nth + (30° * i)), (2; nth + (30° * i)) + (2; nth + (30° * i) - rth)]" a1="i" a2="0" a3="n"/>
<output a0="list5"/>
</command>
<element type="list" label="list5">
<show object="true" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="9" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="CircleArc[(or1; nth + (30° * i) + 15°), (r1; nth + (30° * i) - rth / 2), (or1 + hr1; nth + (30° * i) + 15°)]" a1="i" a2="0" a3="n"/>
<output a0="list6"/>
</command>
<element type="list" label="list6">
<show object="true" label="false" ev="4"/>
<objColor r="204" g="153" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="9" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<element type="boolean" label="move">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="350" y="60"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="204" g="0" b="0" alpha="1.0"/>
<bgColor r="255" g="215" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="34" y="375"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[move, !move] StartAnimation[move]"/>
<font serif="false" sizeM="2.0" size="20" style="1"/>
<caption val="Rotate/Stop"/>
</element>
<element type="image" label="pic1">
<file name="5eb49d1c00bc468008c7fc715a918cb8\Choucj的英文署名.jpg"/>
<inBackground val="false"/>
<absoluteScreenLocation x="324" y="439"/> <show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
</element>
</construction>
</geogebra>