3D Surface and Geometric Construction Visualization of Power Function x^y
2018-05-18 01:11
This GeoGebra example demonstrates the 3D surface graph and related geometric constructions of the power function x^y. Using commands such as Surface, Plane, and CurveCartesian, it builds the spatial surface of the power function, combined with Polygon and PolyLine for auxiliary geometric figures. Parameters like showR and showTheta enable polar or parametric representations. List objects listx an
In collections
Interactive 3D Surfaces in GeoGebra
<?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>