正多边形在直线上的滚动轨迹演示
2020-07-19 02:40
本GeoGebra范例动态演示了正多边形沿直线滚动的几何过程。通过多边形、线段、旋转和重心等命令，结合滑块参数控制，直观展示了正多边形顶点及重心在滚动过程中的运动轨迹。该模型有助于理解刚体平面运动、旋转变换以及轨迹方程的几何意义，适用于中学及大学几何与运动学教学。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.591.0" app="classic" platform="w" id="f5487138-4852-4574-8cc1-b518ef500938" xsi:noNamespaceSchemaLocation="https://ggb123.cn/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1334" height="497" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.18440779610194902" 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="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="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="1" visible="true" inframe="false" stylebar="true" location="1" size="1080" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="true" location="3" size="246" 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="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1" size="400" 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="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="true" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="18"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1080" height="497"/>
<coordSystem xZero="157.59997165514457" yZero="339.44544101035314" scale="27.582248854900506" yscale="27.58224885490047"/>
<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" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="n">
<value val="5"/>
<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="3" max="30" absoluteScreenLocation="true" width="120" x="44" y="44" fixed="false" horizontal="true" showAlgebra="true"/>
<pointSize val="3"/>
<lineStyle thickness="6" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="a">
<value val="20"/>
<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="0" max="20" absoluteScreenLocation="true" width="120" x="39" y="91" fixed="false" horizontal="true" showAlgebra="true"/>
<pointSize val="3"/>
<lineStyle thickness="6" type="0" typeHidden="1"/>
<animation step="0.01" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="b">
<value val="3.88"/>
<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="0" max="5" absoluteScreenLocation="true" width="120" x="37" y="141" fixed="false" horizontal="true" showAlgebra="true"/>
<pointSize val="3"/>
<lineStyle thickness="6" type="0" typeHidden="1"/>
<animation step="0.01" speed="1" type="0" playing="true"/>
</element>
<expression label="f" exp="y = 0" type="line"/>
<element type="line" label="f">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="1" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="explicit"/>
</element>
<command name="Polygon">
<input a0="(0, 0)" a1="(b, 0)" a2="n"/>
<output a0="t"/>
</command>
<element type="polygon" label="t">
<lineStyle thickness="3" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Segment">
<input a0="(b, 0)" a1="(a + b, 0)"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="20" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(0, 0)" a1="(b, 0)"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="3.88" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="c" exp="floor(j / g)" />
<element type="numeric" label="c">
<value val="5"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
</element>
<expression label="d" exp="j / g - c" />
<element type="numeric" label="d">
<value val="0.1546391752577323"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
</element>
<command name="Rotate">
<input a0="Translate[t, Vector[((c * g), 0)]]" a1="(((-(360°))) / n * d)" a2="Translate[(b, 0), Vector[((c * g), 0)]]"/>
<output a0="t1"/>
</command>
<element type="polygon" label="t1">
<lineStyle thickness="3" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Centroid">
<input a0="t1"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<trace val="true"/>
<coords x="3402.13749888669" y="465.3660397170832" z="155.40452987655922"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
</construction>
</geogebra>