幂函数 x^y 的三维曲面与几何构造可视化
2018-05-18 01:11
本 GeoGebra 范例演示幂函数 x^y 的三维曲面图形及其相关几何构造。通过 Surface、Plane、CurveCartesian 等命令构建幂函数的空间曲面，结合 Polygon、PolyLine 绘制辅助几何图形，并利用 showR、showTheta 等参数展示极坐标或参数化表示。listx、listy 列表对象用于生成离散数据点序列，帮助观察幂函数在不同底数与指数下的变化趋势。该范例融合了函数图像绘制、立体几何曲面构造与参数方程等多种数学工具，适合用于高等数学或数学分析课程中幂函数性质的直观教学与探索。
所属专题
GeoGebra曲面互动教学资源集
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.464.0" app="classic" platform="w" id="98716D0A-0397-452B-923F-A703C693730A" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="896" height="648" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.9977678571428571" orientation="1" />
</panes>
<views>
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 | 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3,3" size="300" 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="true" location="1,1" size="300" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3,0" size="339" window="100,100,250,400" />
<view id="1" visible="false" inframe="false" stylebar="false" location="3" size="263" 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="true" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="true" stylebar="true" location="1" size="406" window="685,60,700,550" />
<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" />
<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="true" inframe="false" stylebar="true" location="3" size="894" window="100,100,600,400" />
</views>
<toolbar show="false" 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="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="263" height="543"/>
<coordSystem xZero="125.49333509670709" yZero="96.41232353961631" scale="39.987156559186936" yscale="39.9871565591869"/>
<evSettings axes="true" 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="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="0" yZero="0" zZero="-0.8000479877347428" scale="95.28041000689215" xAngle="29" zAngle="407.2038479800992"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="3"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="2" showNumbers="false" positiveAxis="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="2" showNumbers="false"/>
<axis id="2" show="true" label="" unitLabel="" tickStyle="2" showNumbers="false"/>
<plate show="false"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="1"/>
<projection type="1"/>
</euclidianView3D>
<construction title="x^y" author="" date="">
<expression label ="w" exp="(0, 0, 1)" type="vector"/>
<element type="vector3d" label="w">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="0" y="0" z="1" w="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
</element>
<command name="Point">
<input a0="zAxis"/>
<output a0="C"/>
</command>
<element type="point3d" label="C">
<show object="true" label="false" ev="4"/>
<condition showObject="showTheta"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="0" y="0" z="3" w="1"/>
<pointSize val="5"/>
</element>
<expression label ="O" exp="(0, 0, 0)" type="point"/>
<element type="point3d" label="O">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="0" y="0" z="0" w="1"/>
<pointSize val="5"/>
</element>
<expression label ="u" exp="(1, 0, 0)" type="vector"/>
<element type="vector3d" label="u">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="1" y="0" z="0" w="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
</element>
<command name="Point">
<input a0="Ray[O, O - u]"/>
<output a0="D"/>
</command>
<element type="point3d" label="D">
<show object="true" label="false" ev="4"/>
<objColor r="192" g="192" b="192" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-2" y="0" z="0" w="1"/>
<pointSize val="5"/>
</element>
<command name="Distance">
<input a0="O" a1="D"/>
<output a0="r"/>
</command>
<element type="numeric" label="r">
<value val="2"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="f" exp="f(x) = sqrt(r^(2) - x^(2))" />
<element type="function" label="f">
<show object="false" label="false" ev="4"/>
<objColor r="102" g="102" b="102" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
</element>
<expression label ="v" exp="(0, 1, 0)" type="vector"/>
<element type="vector3d" label="v">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="0" y="1" z="0" w="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
</element>
<command name="Point">
<input a0="Segment[O - (r * v), O + (r * v)]"/>
<output a0="F"/>
</command>
<element type="point3d" label="F">
<show object="true" label="false" ev="4"/>
<condition showObject="showY"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="0" y="-1.5231452054054193" z="0" w="1"/>
<pointSize val="5"/>
</element>
<expression label="k" exp="y(F)" />
<element type="numeric" label="k">
<value val="-1.5231452054054193"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Point">
<input a0="Segment[O, O + (r * u)]"/>
<output a0="E"/>
</command>
<element type="point3d" label="E">
<show object="true" label="false" ev="4"/>
<condition showObject="showX"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="0.4517937403554666" y="0" z="0" w="1"/>
<pointSize val="5"/>
</element>
<expression label="b" exp="x(E)" />
<element type="numeric" label="b">
<value val="0.4517937403554666"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="g" exp="g(x, y) = x^(2) + y^(2) ≤ r^(2)" />
<element type="functionNVar" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="160" g="160" b="160" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="0" type="20" typeHidden="2"/>
</element>
<expression label="c" exp="x = b" type="plane" />
<element type="plane3d" label="c">
<show object="false" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1" y="0" z="0" w="-0.4517937403554666"/>
<fading val="0.1"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<eqnStyle style="user"/>
</element>
<expression label="a" exp="a(x, y) = x^(y) / g(x, y)" />
<element type="functionNVar" label="a">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="0" type="20" typeHidden="2"/>
</element>
<command name="IntersectPath">
<input a0="c" a1="a"/>
<output a0="d"/>
</command>
<element type="implicitpoly" label="d">
<show object="true" label="false" ev="4"/>
<condition showObject="showX"/>
<objColor r="255" g="204" b="51" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<userinput show="false"/></element>
<expression label="e" exp="y = k" type="plane" />
<element type="plane3d" label="e">
<show object="false" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="1" z="0" w="1.5231452054054193"/>
<fading val="0.1"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<eqnStyle style="user"/>
</element>
<command name="IntersectPath">
<input a0="e" a1="a"/>
<output a0="path1"/>
</command>
<element type="implicitpoly" label="path1">
<show object="true" label="false" ev="4"/>
<condition showObject="showY"/>
<objColor r="255" g="255" b="102" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<userinput show="false"/></element>
<expression label="h" exp="x^(2) + y^(2) = r^(2)" type="quadric" />
<element type="quadric" label="h">
<show object="true" label="false" ev="8"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="0" A3="-4" A4="0" A5="0" A6="0" A7="0" A8="0" A9="0"/>
<eqnStyle style="user"/>
</element>
<command name="Point">
<input a0="Semicircle[(0, r), (0, (-r))]"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="false" ev="4"/>
<condition showObject="showTheta"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="1.7629665361929563" y="0.9444305121414756" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Plane">
<input a0="A" a1="(0, 0, 0)" a2="(0, 0, 1)"/>
<output a0="i"/>
</command>
<element type="plane3d" label="i">
<show object="false" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.9444305121414756" y="1.7629665361929563" z="0" w="0"/>
<fading val="0.1"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<command name="IntersectPath">
<input a0="i" a1="a"/>
<output a0="j"/>
</command>
<element type="implicitpoly" label="j">
<show object="true" label="false" ev="4"/>
<condition showObject="showTheta"/>
<objColor r="255" g="204" b="51" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="4" type="0" typeHidden="2" opacity="178"/>
<userinput show="false"/></element>
<command name="Point">
<input a0="Segment[A, (0, 0)]"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="false" ev="4"/>
<condition showObject="showR"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0.9418862214215029" y="0.5045734381306195" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Distance">
<input a0="B" a1="O"/>
<output a0="r2"/>
</command>
<element type="numeric" label="r2">
<value val="1.0685242199270124"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="l" exp="x^(2) + y^(2) = r2^(2)" type="quadric" />
<element type="quadric" label="l">
<show object="false" label="false" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="0" A3="-1.1417440085706303" A4="0" A5="0" A6="0" A7="0" A8="0" A9="0"/>
<eqnStyle style="user"/>
</element>
<command name="Surface">
<input a0="(r2 * cos(t))" a1="(r2 * sin(t))" a2="(a((r2 * cos(t)), (r2 * sin(t))) * s)" a3="t" a4="((-π)) / 2" a5="π / 2" a6="s" a7="0" a8="1"/>
<output a0="m"/>
</command>
<element type="surfacecartesian3d" label="m">
<show object="true" label="false" ev="4"/>
<condition showObject="showR"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="20" typeHidden="2"/>
</element>
<command name="CurveCartesian">
<input a0="(r2 * cos(t))" a1="(r2 * sin(t))" a2="a((r2 * cos(t)), (r2 * sin(t)))" a3="t" a4="((-π)) / 2" a5="π / 2"/>
<output a0="n"/>
</command>
<element type="curvecartesian3d" label="n">
<show object="true" label="false" ev="5"/>
<condition showObject="showR"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="2"/>
</element>
<command name="Polygon">
<input a0="{O, A, A + C, C}"/>
<output a0="q1"/>
</command>
<element type="polygon3d" label="q1">
<lineStyle thickness="0" type="0" typeHidden="2" opacity="178"/>
<show object="true" label="false" ev="5"/>
<condition showObject="showTheta"/>
<objColor r="191" g="255" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="PolyLine">
<input a0="O" a1="A" a2="A + C" a3="C" a4="O"/>
<output a0="p"/>
</command>
<element type="polyline3d" label="p">
<lineStyle thickness="2" type="0" typeHidden="2" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showTheta"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="CurveCartesian">
<input a0="(r * cos(t))" a1="(r * sin(t))" a2="a((r * cos(t)), (r * sin(t)))" a3="t" a4="((-π)) / 2" a5="π / 2"/>
<output a0="o"/>
</command>
<element type="curvecartesian3d" label="o">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="3" type="0" typeHidden="2"/>
</element>
<element type="boolean" label="showR">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="boolean" label="showTheta">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="q" exp="x^(2) + y^(2) = r^(2)" type="conic" />
<element type="conic" label="q">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-4" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<expression label="listx" exp="O + (b * u) + {(f(b) * v), (f(b) * v) + (z(C) * w), ((-f(b)) * v) + (z(C) * w), ((-f(b)) * v)}" />
<element type="list" label="listx">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Polygon">
<input a0="listx"/>
<output a0="q2"/>
</command>
<element type="polygon3d" label="q2">
<lineStyle thickness="0" type="0" typeHidden="2" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showX"/>
<objColor r="99" g="219" b="219" alpha="0.44999998807907104"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<expression label="q3" exp="q2" />
<element type="polygon3d" label="q3">
<lineStyle thickness="1" type="0" typeHidden="2" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showX"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="boolean" label="showX">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="listy" exp="O + (k * v) + {(f(abs(k)) * u), (f(abs(k)) * u) + (z(C) * w), (z(C) * w), (0 * u)}" />
<element type="list" label="listy">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Polygon">
<input a0="listy"/>
<output a0="q4"/>
</command>
<element type="polygon3d" label="q4">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showY"/>
<objColor r="153" g="204" b="255" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<expression label="q5" exp="q4" />
<element type="polygon3d" label="q5">
<lineStyle thickness="1" type="0" typeHidden="2" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showY"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="boolean" label="showY">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="PolyLine">
<input a0="O + (b * u) + (k * v) + {(0 * u), (z(C) * w)}"/>
<output a0="segXY"/>
</command>
<element type="polyline3d" label="segXY">
<lineStyle thickness="1" type="0" typeHidden="2" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showX ∧ showY"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<expression label="text1" exp=""\text{" + (LaTeX[If[showR, "✅", " "]]) + " } r=" + (LaTeX[r2]) + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="5"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="16" y="17"/>
<ggbscript val="SetValue(showR, !showR)"/>
</element>
<expression label="text2" exp=""\text{ " + (LaTeX[If[showTheta, "✅", " "]]) + " } θ= " + (LaTeX[If[Angle[A] > π, Angle[A] - (2 * π), Angle[A]]]) + """ />
<element type="text" label="text2">
<show object="true" label="false" ev="5"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="7" y="51"/>
<ggbscript val="SetValue(showTheta, !showTheta)"/>
</element>
<expression label="text3" exp=""\text{" + (LaTeX[If[showX, "✅", " "]]) + " } x=" + (LaTeX[b]) + """ />
<element type="text" label="text3">
<show object="true" label="false" ev="5"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="12" y="86"/>
<ggbscript val="SetValue(showX, !showX)"/>
</element>
<expression label="text4" exp=""\text{" + (LaTeX[If[showY, "✅", " "]]) + " } y=" + (LaTeX[k]) + """ />
<element type="text" label="text4">
<show object="true" label="false" ev="5"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="13" y="119"/>
<ggbscript val="SetValue(showY, !showY)"/>
</element>
<expression label="text5" exp=""x^y""/>
<element type="text" label="text5">
<show object="true" label="false" ev="37"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="8" size="112" style="1"/>
<absoluteScreenLocation x="694" y="15"/>
</element>
</construction>
</geogebra>