龟兔赛跑主题几何作图与孔位动态演示画板
2020-01-28 09:24
本范例展示了一个以“龟兔赛跑”为主题的动态几何画板。用户可以通过拖动滑动条b来动态选择图形中“孔”的位置。画板综合运用了圆、线段、射线、半圆及旋转等几何构造命令，探讨了周期重合度、孔距以及小圆半径等参数对图形形态的影响。该范例生动演示了复杂几何图形的构造过程，并通过交互式滑块直观呈现了参数变化带来的几何变换效果，适合用于几何作图与动态数学演示的教学。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.574.0" app="classic" platform="w" id="510289C1-6499-47FB-8E58-59F77D89AEF4" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="768" height="905" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.3567708333333333" 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="320" window="100,100,700,550" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="768" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="274" 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="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="2"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="768" height="852"/>
<coordSystem xZero="320.41104730800487" yZero="434.8221431623637" scale="29.161506141301892" yscale="29.161506141301896"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3" lockedAxesRatio="1"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="9" grid="0"/>
<axis id="0" show="false" label="x" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="y" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<algebraView>
<mode val="3"/>
<auxiliary show="true"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="3" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="模拟龟兔画板" author="" date="">
<element type="numeric" label="小圆半径">
<value val="4"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="7" absoluteScreenLocation="true" width="200" x="16" y="112" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="a">
<value val="4769.3"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="15" y="-1"/>
<labelMode val="1"/>
<slider min="0" max="5000" absoluteScreenLocation="true" width="200" x="21" y="25" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="0.02" type="0" playing="true"/>
</element>
<command name="Point">
<input a0="xAxis"/>
<output a0="O"/>
</command>
<element type="point" label="O">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-32" y="6"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="A" exp="(7 - 小圆半径, 0)" type="point" />
<element type="point" label="A">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="3" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="周期重合度">
<value val="0.09"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0.03" max="0.09" absoluteScreenLocation="true" width="200" x="28" y="163" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<command name="Rotate">
<input a0="A" a1="((周期重合度 * a))°" a2="O"/>
<output a0="Z"/>
</command>
<element type="point" label="Z">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.063509612975203" y="2.80516439858867" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="孔距">
<value val="2.6"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="4" absoluteScreenLocation="true" width="200" x="19" y="72" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<command name="Rotate">
<input a0="Z" a1="((小圆半径 * a))°" a2="O"/>
<output a0="A'"/>
</command>
<element type="point" label="A'">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.1992715636710627" y="2.7498632177928353" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="P" exp="(7, 0)" type="point"/>
<element type="point" label="P">
<show object="false" label="true"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="7" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="O" a1="P"/>
<output a0="c_1"/>
</command>
<element type="conic" label="c_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="7" 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="-49" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="Circle[A', 小圆半径]"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="-2.5196583755107285" y="4.222805887232933" z="1"/>
<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="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.4729426694400973" y="-3.718929939181791" z="11.993006907681808"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="B" a1="(-(((7 * a) - (小圆半径 * a))°))" a2="A'"/>
<output a0="B'"/>
</command>
<element type="point" label="B'">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.13640648291691182" y="-1.0205431470255424" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="A'" a1="B'"/>
<output a0="d_1"/>
</command>
<element type="conic" label="d_1">
<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="-6.999999999999998" A3="0" A4="-1.1992715636710627" A5="-2.7498632177928353"/>
<eqnStyle style="specific"/>
</element>
<command name="Rotate">
<input a0="B'" a1="45°" a2="A'"/>
<output a0="B''"/>
</command>
<element type="point" label="B''">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.920884467838699" y="-0.8606836948235177" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Angle">
<input a0="B'" a1="A'" a2="B''"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="0"/>
<value val="0.7853981633974482"/>
<show object="false" label="true"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="2"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
</element>
<command name="Ray">
<input a0="A'" a1="B''"/>
<output a0="g"/>
</command>
<element type="ray" label="g">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.610546912616353" y="1.7216129041676362" z="-9.064226242049227"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Circle">
<input a0="A'" a1="孔距"/>
<output a0="e"/>
</command>
<element type="conic" label="e">
<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="2.240000000000002" A3="0" A4="-1.1992715636710627" A5="-2.7498632177928353"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="e" a1="g" a2="1"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-10" y="52"/>
<labelMode val="0"/>
<trace val="true"/>
<coords x="2.3183199513800266" y="0.4030077245922059" z="1"/>
<pointSize val="1"/>
<pointStyle val="10"/>
</element>
<command name="Line">
<input a0="B'" a1="A'"/>
<output a0="h"/>
</command>
<element type="line" label="h">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.7704063648183777" y="1.3356780465879745" z="0.8488092056854069"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="d_1" a1="h" a2="2"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.534949610259037" y="6.520269582611213" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Semicircle">
<input a0="D" a1="B'"/>
<output a0="k"/>
</command>
<element type="conicpart" label="k">
<show object="false" label="false"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="7" 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="-6.9999999999999964" A3="0" A4="-1.1992715636710627" A5="-2.7498632177928357"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Semicircle">
<input a0="B'" a1="D"/>
<output a0="p"/>
</command>
<element type="conicpart" label="p">
<show object="false" label="false"/>
<objColor r="153" g="51" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="7" 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="-6.9999999999999964" A3="0" A4="-1.1992715636710627" A5="-2.7498632177928357"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>