圆在直线上的滚动演示
2019-11-10 01:10
本范例演示了一个圆在直线上滚动的几何过程。通过GeoGebra的旋转、交点和距离等工具，直观展示了圆在直线上纯滚动时，圆心轨迹、圆上特定点的运动轨迹（如摆线）以及滚动距离与圆弧长度的关系。适合用于几何作图、运动轨迹及图形变换的数学教学与探索。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.564.0" app="classic" platform="d" id="421fff6c-bfda-4d18-8104-e46022eb5c8d" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1936" height="1056" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.7975206611570248" 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 , 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 || 1008 1009 || 66 68 || 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="3" size="1909" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="330" window="100,100,600,400" />
<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" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1" size="360" window="100,100,700,550" />
<view id="70" 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="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1909" height="885"/>
<coordSystem xZero="131.49999999999997" yZero="485.5" scale="49.99999999999998" yscale="49.99999999999998"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<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="0" spreadsheet="0"/>
<coordStyle val="0"/>
<startAnimation val="true"/>
</kernel>
<tableview min="-2.0" max="2.0" step="1.0"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="A">
<show object="true" label="true"/>
<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"/>
<coords x="6.66" y="0.5" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="true" 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"/>
<coords x="23.94" y="0.48" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.020000000000000018" y="17.28" z="-8.773200000000001"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="true"/>
<coords x="11.767062680224974" y="0.4940890478238137" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="OrthogonalLine">
<input a0="C" a1="f"/>
<output a0="g"/>
</command>
<element type="line" label="g">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-17.28" y="0.020000000000000018" z="203.3249613333311"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<element type="point" label="D">
<show object="false" label="true"/>
<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"/>
<coords x="8.78" y="4.76" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="E">
<show object="false" label="true"/>
<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"/>
<coords x="10.72" y="4.72" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="D" a1="E"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.040000000000000036" y="1.9400000000000013" z="-9.585600000000007"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Distance">
<input a0="D" a1="E"/>
<output a0="距离DE"/>
</command>
<element type="numeric" label="距离DE">
<value val="1.9404123273160283"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="文本DE" exp="Name[D] + (Name[E]) + " = " + 距离DE" />
<element type="text" label="文本DE">
<show object="false" label="true" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="Midpoint[D, E]"/>
</element>
<command name="Circle">
<input a0="C" a1="h"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<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="134.9426881075228" A3="0.0" A4="-11.767062680224974" A5="-0.4940890478238137"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="c" a1="g"/>
<output a0="F" a1="G"/>
</command>
<element type="point" label="F">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="11.764816834128172" y="-1.4463219798131908" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="G">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-27" y="4"/>
<labelMode val="0"/>
<coords x="11.769308526321776" y="2.434500075460818" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="c" a1="g" a2="2"/>
<output a0="H"/>
</command>
<element type="point" label="H">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="25" y="-4"/>
<labelMode val="0"/>
<coords x="11.769308526321776" y="2.434500075460818" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="G" a1="C"/>
<output a0="d"/>
</command>
<element type="conic" label="d">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<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="140.6782138051692" A3="0.0" A4="-11.769308526321776" A5="-2.434500075460818"/>
<eqnStyle style="specific"/>
</element>
<command name="Distance">
<input a0="C" a1="A"/>
<output a0="距离CA"/>
</command>
<element type="numeric" label="距离CA">
<value val="5.1070661009137455"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="文本CA" exp="Name[C] + (Name[A]) + " = " + 距离CA" />
<element type="text" label="文本CA">
<show object="false" label="true" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="Midpoint[C, A]"/>
<labelOffset x="-68" y="42"/>
</element>
<command name="Distance">
<input a0="G" a1="C"/>
<output a0="距离GC"/>
</command>
<element type="numeric" label="距离GC">
<value val="1.9404123273160232"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="文本GC" exp="Name[G] + (Name[C]) + " = " + 距离GC" />
<element type="text" label="文本GC">
<show object="false" label="true" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="Midpoint[G, C]"/>
</element>
<command name="Distance">
<input a0="A" a1="C"/>
<output a0="AC"/>
</command>
<element type="numeric" label="AC">
<value val="5.1070661009137455"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<auxiliary val="true"/>
</element>
<command name="Distance">
<input a0="G" a1="C"/>
<output a0="GC"/>
</command>
<element type="numeric" label="GC">
<value val="1.9404123273160232"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<auxiliary val="true"/>
</element>
<expression label="a" exp="AC / GC" />
<element type="numeric" label="a">
<value val="2.6319489054049843"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<element type="point" label="I">
<show object="false" label="true"/>
<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"/>
<coords x="9.68" y="0.84" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="C" a1="(-a)" a2="G"/>
<output a0="C'"/>
</command>
<element type="point" label="C'">
<show object="true" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="10.824607819849508" y="4.129416172260534" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="G" a1="C'"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.6949160967997159" y="-0.9447007064722683" z="22.24786441065955"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="J">
<show object="false" label="true"/>
<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"/>
<coords x="8.92" y="6.82" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="C'" a1="(-(120°))" a2="G"/>
<output a0="C''"/>
</command>
<element type="point" label="C''">
<show object="true" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="13.709499276669629" y="2.405176837839051" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="G" a1="C''"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.029323237621766918" y="1.9401907503478526" z="-5.068508758691447"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="C''" a1="(-(120°))" a2="G"/>
<output a0="C'''"/>
</command>
<element type="point" label="C'''">
<show object="true" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="10.773818482446192" y="0.7689072162828692" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="G" a1="C'''"/>
<output a0="k"/>
</command>
<element type="segment" label="k">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.6655928591779487" y="-0.9954900438755843" z="-17.179355651968095"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>