完全图及其几何变换
2020-08-27 09:06
本GeoGebra范例展示了完全图的构造及其几何变形过程。通过运用Sequence和Flatten等命令，动态生成多边形顶点间的连线，构建出任意四边形或多边形的完全图结构。范例结合了几何变换与曲线构图，直观演示了顶点数与连线数之间的关系，以及外接圆在图形构造中的应用，适合用于图论基础与几何变换的教学与探索。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.596.0" app="classic" platform="d" id="008ec657-d646-4962-b877-be7a861f2ec4" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1920" height="1040" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.790625" orientation="1" />
<pane location="0" divider="0.22604166666666667" orientation="1" />
</panes>
<views>
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="3,1,3" size="481" window="100,100,600,400" />
<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="1,1,1" size="500" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="3,1" size="1079" 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="true" location="1,1" size="300" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="true" location="3,3" size="434" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="994" 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="false" location="1" size="150" window="50,50,500,500" />
<view id="4097" visible="true" inframe="false" stylebar="true" location="1" size="370" 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 | 100002 100001" position="1" help="false" />
<input show="true" cmd="true" top="true" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="18"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1079" height="808"/>
<coordSystem xZero="595.7846284890807" yZero="453.20462854465285" scale="94.5685861012724" yscale="94.56856946852402"/>
<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="11" grid="0"/>
<labelStyle axes="0" serif="true"/>
<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"/>
<auxiliary show="true"/>
</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"/>
<construction title="" author="" date="">
<element type="numeric" label="n">
<value val="16.0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="3" max="30" absoluteScreenLocation="true" width="200.0" x="62.0" y="127.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<ggbscript onUpdate=""/>
</element>
<element type="numeric" label="k">
<value val="1.21"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="2" absoluteScreenLocation="true" width="200.0" x="66.0" y="194.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.01" speed="1" type="0" playing="false"/>
<ggbscript onUpdate=""/>
</element>
<element type="point" label="A">
<show object="true" 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="-1.1820482159833923" y="-0.2621946339539368" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" 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="1.0808596778792678" y="-0.2516202961414901" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Rotate[B, (360° * i / n), A]" a1="i" a2="1" a3="n"/>
<output a0="l1"/>
</command>
<element type="list" label="l1">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" 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="Sequence">
<input a0="Sequence[Segment[l1(i), l1(j)], j, i + 1, n]" a1="i" a2="1" a3="n - 1"/>
<output a0="l2"/>
</command>
<element type="list" label="l2">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" 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="Flatten">
<input a0="l2"/>
<output a0="l3"/>
</command>
<element type="list" label="l3">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" 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="Sequence">
<input a0="Dilate[l3(i), k, Midpoint[l3(i)]]" a1="i" a2="1" a3="Length[l3]"/>
<output a0="l4"/>
</command>
<element type="list" label="l4">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" 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>
<expression label="text1" exp=""完全图及其变形""/>
<element type="text" label="text1">
<show object="true" label="true" ev="40"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<bgColor r="208" g="240" b="192" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="18" style="1"/>
<startPoint x="-2.916239312214589" y="4.33764231446035" z="1.0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
</element>
<expression label="text2" exp=""仿自金晓亮老师""/>
<element type="text" label="text2">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="188" g="212" b="230" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="0"/>
<startPoint x="-1.996272084335844" y="3.576289991964192" z="1.0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
</element>
<expression label="text3" exp=""制作：卢德洪\\
\quad2020.8.27""/>
<element type="text" label="text3">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="0"/>
<startPoint x="2.3074826483842634" y="4.316493638835456" z="1.0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
</element>
</construction>
</geogebra>