二重积分与黎曼和可视化
2015-01-08 03:45
本范例演示了二元函数二重积分的几何意义及其黎曼和近似计算过程。通过构建长方体网格，直观展示了在给定区域上对函数进行积分时，底面积与函数值乘积的累加过程，帮助理解二重积分的概念与计算方法。
所属专题
微积分
GeoGebra 画板及绘图内容加载中，请稍等……
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.42.0" id="218110f9-e84c-4a0b-97de-db48999b2766" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="823" height="657" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.2332928311057108" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="585,299,855,601" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3,3" size="300" window="100,100,600,400" />
<view id="1" visible="false" inframe="true" stylebar="true" location="3,3" size="185" window="746,461,600,391" />
<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="1,1" size="300" window="100,100,600,400" />
<view id="2" visible="false" inframe="true" stylebar="true" location="3" size="200" window="1005,24,250,598" />
<view id="16" visible="false" inframe="false" stylebar="false" location="3" size="192" 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="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" 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 , 22 , 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="1" size="812" window="100,100,600,400" />
</views>
<toolbar show="true" items="0 39 | 1 501 67 , 5 19 , 72 | 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 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="false" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="12"/>
<graphicsSettings javaLatexFonts="false"/>
<consProtColumns col0="true" col1="true" col2="false" col3="true" col4="false" col5="true" col6="true" col7="false"/>
<consProtocol useColors="true" addIcons="false" showOnlyBreakpoints="false"/>
<consProtNavigationBar show="true" playButton="true" playDelay="2.0" protButton="true" consStep="73"/>
</gui>
<euclidianView>
<size width="600" height="303"/>
<coordSystem xZero="215.0" yZero="315.00000000000006" scale="50.0" yscale="50.00000000000002"/>
<evSettings axes="true" grid="true" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<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="10"/>
<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"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="-3.1303948070975967" yZero="-4.122037739720619" zZero="-2.842083590937114" scale="50.07272727272729" xAngle="20.0" zAngle="1846.5324205153756"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="0" rightAngleStyle="1" gridType="0"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="2" showNumbers="false"/>
<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="0"/>
<projection type="1"/>
</euclidianView3D>
<construction title="" author="" date="">
<command name="Point">
<input a0="yAxis"/>
<output a0="Y1"/>
</command>
<element type="point" label="Y1">
<show object="true" label="false"/>
<objColor r="102" g="204" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.0" y="0.9164848262896865" z="1.0"/>
<coordStyle style="cartesian3d"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="yAxis"/>
<output a0="Y2"/>
</command>
<element type="point" label="Y2">
<show object="true" label="false"/>
<objColor r="102" g="204" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.0" y="5.714835619880109" z="1.0"/>
<coordStyle style="cartesian3d"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="xAxis"/>
<output a0="X1"/>
</command>
<element type="point" label="X1">
<show object="true" label="false"/>
<objColor r="102" g="204" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="5.661681386305523" y="0.0" z="1.0"/>
<coordStyle style="cartesian3d"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="xAxis"/>
<output a0="X2"/>
</command>
<element type="point" label="X2">
<show object="true" label="false"/>
<objColor r="102" g="204" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.8273301278736853" y="0.0" z="1.0"/>
<coordStyle style="cartesian3d"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Min">
<input a0="x(X1)" a1="x(X2)"/>
<output a0="a1"/>
</command>
<element type="numeric" label="a1">
<value val="0.8273301278736853"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Max">
<input a0="x(X1)" a1="x(X2)"/>
<output a0="a2"/>
</command>
<element type="numeric" label="a2">
<value val="5.661681386305523"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Min">
<input a0="y(Y1)" a1="y(Y2)"/>
<output a0="b1"/>
</command>
<element type="numeric" label="b1">
<value val="0.9164848262896865"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Max">
<input a0="y(Y1)" a1="y(Y2)"/>
<output a0="b2"/>
</command>
<element type="numeric" label="b2">
<value val="5.714835619880109"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="P1" exp="(a1, b1)" type="point" />
<element type="point" label="P1">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0.8273301278736853" y="0.9164848262896865" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="P2" exp="(a2, b1)" type="point" />
<element type="point" label="P2">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="5.661681386305523" y="0.9164848262896865" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="P3" exp="(a2, b2)" type="point" />
<element type="point" label="P3">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="5.661681386305523" y="5.714835619880109" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="P4" exp="(a1, b2)" type="point" />
<element type="point" label="P4">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0.8273301278736853" y="5.714835619880109" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="P1" a1="P2" a2="P3" a3="P4"/>
<output a0="poly1" a1="p1" a2="p2" a3="p3" a4="p4"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="96" g="96" b="96" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="segment" label="p1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="0.0" y="4.8343512584318376" z="-4.430609573307231"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="p2">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="-4.798350793590423" y="0.0" z="27.166733373035232"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="p3">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="0.0" y="-4.8343512584318376" z="27.627522770698498"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="p4">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="4.798350793590423" y="0.0" z="-3.9698201756439637"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="X2" a1="P1"/>
<output a0="seg01"/>
</command>
<element type="segment" label="seg01">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-0.9164848262896865" y="0.0" z="0.7582355085285386"/>
<lineStyle thickness="1" type="20" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="X1" a1="P2"/>
<output a0="seg02"/>
</command>
<element type="segment" label="seg02">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-0.9164848262896865" y="0.0" z="5.188845081835769"/>
<lineStyle thickness="1" type="20" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="Y1" a1="P1"/>
<output a0="seg03"/>
</command>
<element type="segment" label="seg03">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0.0" y="0.8273301278736853" z="-0.7582355085285386"/>
<lineStyle thickness="1" type="20" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="Y2" a1="P4"/>
<output a0="seg04"/>
</command>
<element type="segment" label="seg04">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0.0" y="0.8273301278736853" z="-4.728055684172502"/>
<lineStyle thickness="1" type="20" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="numeric" label="k">
<value val="-0.18"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="204" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="200.0" x="30.0" y="50.0" fixed="true" horizontal="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.01" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="a">
<value val="2.1442688148476576"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="200.0" x="30.0" y="90.0" fixed="true" horizontal="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="b">
<value val="2.5074447073385526"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="200.0" x="30.0" y="130.0" fixed="true" horizontal="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="h">
<value val="5.0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="200.0" x="30.0" y="170.0" fixed="true" horizontal="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<expression label="f" exp="f(x, y) = (k * ((x - a)^(2) + (y - b)^(2) / 2)) + h" />
<element type="functionNVar" label="f">
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Function">
<input a0="f(s, t)" a1="s" a2="a1" a3="a2" a4="t" a5="b1" a6="b2"/>
<output a0="f2"/>
</command>
<element type="functionNVar" label="f2">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<levelOfDetail val="5"/>
</element>
<element type="vector3d" label="u_i">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="1.0" y="0.0" z="0.0" w="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<element type="vector3d" label="u_j">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="0.0" y="1.0" z="0.0" w="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<element type="vector3d" label="u_k">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="0.0" y="0.0" z="1.0" w="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<expression label="Q1" exp="P1 + (f(P1) * u_k)" type="point" />
<element type="point3d" label="Q1">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0.8273301278736853" y="0.9164848262896865" z="4.460017248175596" w="1.0"/>
<pointSize val="3"/>
</element>
<expression label="Q2" exp="P2 + (f(P2) * u_k)" type="point" />
<element type="point3d" label="Q2">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="5.661681386305523" y="0.9164848262896865" z="2.5452017835073977" w="1.0"/>
<pointSize val="3"/>
</element>
<expression label="Q3" exp="P3 + (f(P3) * u_k)" type="point" />
<element type="point3d" label="Q3">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="5.661681386305523" y="5.714835619880109" z="1.8471435024601557" w="1.0"/>
<pointSize val="3"/>
</element>
<expression label="Q4" exp="P4 + (f(P4) * u_k)" type="point" />
<element type="point3d" label="Q4">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0.8273301278736853" y="5.714835619880109" z="3.761958967128354" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Segment">
<input a0="P1" a1="Q1"/>
<output a0="seg05"/>
</command>
<element type="segment3d" label="seg05">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="P2" a1="Q2"/>
<output a0="seg06"/>
</command>
<element type="segment3d" label="seg06">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="P3" a1="Q3"/>
<output a0="seg07"/>
</command>
<element type="segment3d" label="seg07">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="P4" a1="Q4"/>
<output a0="seg08"/>
</command>
<element type="segment3d" label="seg08">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="numeric" label="m">
<value val="6.0"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="10" absoluteScreenLocation="true" width="100.0" x="30.0" y="210.0" fixed="false" horizontal="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="n">
<value val="5.0"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="10" absoluteScreenLocation="true" width="100.0" x="30.0" y="250.0" fixed="false" horizontal="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="dx" exp="(a2 - a1) / m" />
<element type="numeric" label="dx">
<value val="0.8057252097386396"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="dy" exp="(b2 - b1) / n" />
<element type="numeric" label="dy">
<value val="0.9596701587180846"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Sequence">
<input a0="Segment[(a1 + (k * dx), b1), (a1 + (k * dx), b2)]" a1="k" a2="1" a3="m - 1"/>
<output a0="segXs"/>
</command>
<element type="list" label="segXs">
<show object="true" label="false"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="20" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Segment[(a1, b1 + (k * dy)), (a2, b1 + (k * dy))]" a1="k" a2="1" a3="n - 1"/>
<output a0="segYs"/>
</command>
<element type="list" label="segYs">
<show object="true" label="false"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="20" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="PointIn">
<input a0="poly1"/>
<output a0="P"/>
</command>
<element type="point" label="P">
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="2.3104518420725353" y="4.633422351344885" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="x0" exp="x(P)" />
<element type="numeric" label="x0">
<value val="2.3104518420725353"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="y0" exp="y(P)" />
<element type="numeric" label="y0">
<value val="4.633422351344885"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Max">
<input a0="1" a1="ceil((m * (x0 - a1) / (a2 - a1)))"/>
<output a0="m0"/>
</command>
<element type="numeric" label="m0">
<value val="2.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Max">
<input a0="1" a1="ceil((n * (y0 - b1) / (b2 - b1)))"/>
<output a0="n0"/>
</command>
<element type="numeric" label="n0">
<value val="4.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="P5" exp="P1 + (((m0 - 1) * dx), ((n0 - 1) * dy))" type="point" />
<element type="point" label="P5">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="1.633055337612325" y="3.7954953024439404" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="P7" exp="P5 + (dx, dy)" type="point" />
<element type="point" label="P7">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="32" y="-3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="2.4387805473509645" y="4.755165461162025" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="P6" exp="P5 + (dx, 0)" type="point" />
<element type="point" label="P6">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="2.4387805473509645" y="3.7954953024439404" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="P8" exp="P5 + (0, dy)" type="point" />
<element type="point" label="P8">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="1.633055337612325" y="4.755165461162025" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Prism">
<input a0="Polygon[P5, P6, P7, P8]" a1="f(Midpoint[P5, P7])"/>
<output a0="prismP" a1="Q5" a2="Q6" a3="Q7" a4="Q8" a5="faceABP6P5" a6="faceBCP7P6" a7="faceCDP8P7" a8="faceADP8P5" a9="faceABCD" a10="edgeAP5" a11="edgeBP6" a12="edgeCP7" a13="edgeDP8" a14="edgeAB" a15="edgeBC" a16="edgeCD" a17="edgeAD"/>
</command>
<element type="polyhedron" label="prismP">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.4"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="point3d" label="Q5">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.633055337612325" y="3.7954953024439404" z="4.716599037704465" w="1.0"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="Q6">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.4387805473509645" y="3.7954953024439404" z="4.716599037704465" w="1.0"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="Q7">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.4387805473509645" y="4.755165461162025" z="4.716599037704465" w="1.0"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="Q8">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.633055337612325" y="4.755165461162025" z="4.716599037704465" w="1.0"/>
<pointSize val="3"/>
</element>
<element type="polygon3d" label="faceABP6P5">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="255" g="255" b="0" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceBCP7P6">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="255" g="255" b="0" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceCDP8P7">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="255" g="255" b="0" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceADP8P5">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="255" g="255" b="0" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceABCD">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="255" g="255" b="0" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="segment3d" label="edgeAP5">
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBP6">
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeCP7">
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeDP8">
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeAB">
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBC">
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeCD">
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeAD">
<show object="true" label="false"/>
<condition showObject="showPrism"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="CurveCartesian">
<input a0="s" a1="b1" a2="f(s, b1)" a3="s" a4="a1" a5="a2"/>
<output a0="curveY1"/>
</command>
<element type="curvecartesian3d" label="curveY1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
</element>
<command name="CurveCartesian">
<input a0="s" a1="b2" a2="f(s, b2)" a3="s" a4="a1" a5="a2"/>
<output a0="curveY2"/>
</command>
<element type="curvecartesian3d" label="curveY2">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
</element>
<command name="CurveCartesian">
<input a0="a1" a1="s" a2="f(a1, s)" a3="s" a4="b1" a5="b2"/>
<output a0="curveX1"/>
</command>
<element type="curvecartesian3d" label="curveX1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
</element>
<command name="CurveCartesian">
<input a0="a2" a1="s" a2="f(a2, s)" a3="s" a4="b1" a5="b2"/>
<output a0="curveX2"/>
</command>
<element type="curvecartesian3d" label="curveX2">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="0" typeHidden="2"/>
</element>
<element type="boolean" label="showPrism">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="5" y="5"/>
<labelMode val="0"/>
</element>
<command name="Sequence">
<input a0="Sequence[Prism[Polygon[(a1 + ((j - 1) * dx), b1 + ((k - 1) * dy)), (a1 + (j * dx), b1 + ((k - 1) * dy)), (a1 + (j * dx), b1 + (k * dy)), (a1 + ((j - 1) * dx), b1 + (k * dy))], f(a1 + ((j - 1 / 2) * dx), b1 + ((k - 1 / 2) * dy))], k, 1, n]" a1="j" a2="1" a3="m"/>
<output a0="prisms"/>
</command>
<element type="list" label="prisms">
<show object="true" label="false"/>
<condition showObject="¬showPrism"/>
<objColor r="102" g="153" b="255" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="PointIn">
<input a0="z = 0"/>
<output a0="FlagP"/>
</command>
<element type="point3d" label="FlagP">
<show object="true" label="false"/>
<objColor r="153" g="102" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-2.138069506344078" y="5.735156497039938" z="0.0" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Point">
<input a0="Line[FlagP, FlagP + (0, 0, 1)]"/>
<output a0="FlagQ"/>
</command>
<element type="point3d" label="FlagQ">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<ggbscript val="SetValue[showPrism, !showPrism]"/>
<coords x="-2.138069506344078" y="5.735156497039938" z="5.704779394274543" w="1.0"/>
<pointSize val="5"/>
</element>
<command name="Segment">
<input a0="FlagP" a1="FlagQ"/>
<output a0="FlagPole"/>
</command>
<element type="segment3d" label="FlagPole">
<show object="true" label="false"/>
<objColor r="204" g="102" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="txtFlag" exp=""Show Prisms""/>
<element type="text" label="txtFlag">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="FlagQ"/>
<labelOffset x="-77" y="22"/>
<ggbscript val="RunClickScript[FlagQ]"/>
</element>
<command name="Point">
<input a0="FlagPole"/>
<output a0="A"/>
</command>
<element type="point3d" label="A">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-2.138069506344078" y="5.735156497039938" z="0.9818065585998882" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Point">
<input a0="FlagPole"/>
<output a0="B"/>
</command>
<element type="point3d" label="B">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-2.138069506344078" y="5.735156497039938" z="4.361484432782838" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Point">
<input a0="Segment[A, B]"/>
<output a0="Pm"/>
</command>
<element type="point3d" label="Pm">
<show object="true" label="false"/>
<objColor r="51" g="51" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<ggbscript onUpdate="SetValue[m, Max[1, ceil(maxPart*z(Pm-A)/z(B-A))]]"/>
<coords x="-2.138069506344078" y="5.735156497039938" z="2.918589349552644" w="1.0"/>
<pointSize val="3"/>
</element>
<expression label="text1" exp=""m=" + m + """ />
<element type="text" label="text1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="153" g="204" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<startPoint exp="Pm"/>
<labelOffset x="6" y="18"/>
</element>
<command name="Point">
<input a0="Segment[A, B]"/>
<output a0="Pn"/>
</command>
<element type="point3d" label="Pn">
<show object="true" label="false"/>
<objColor r="0" g="204" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<ggbscript onUpdate="SetValue[n, Max[1, ceil(maxPart*z(Pn-A)/z(B-A))]]"/>
<coords x="-2.138069506344078" y="5.735156497039938" z="2.400846101607957" w="1.0"/>
<pointSize val="3"/>
</element>
<expression label="text2" exp=""n=" + n + """ />
<element type="text" label="text2">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="191" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<startPoint exp="Pn"/>
<labelOffset x="-32" y="18"/>
</element>
<element type="numeric" label="maxPart">
<value val="10.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="point" label="FuncCenter">
<show object="true" label="true"/>
<condition showObject="showControls"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue[a, x(FuncCenter)] SetValue[b, y(FuncCenter)]"/>
<coords x="2.1442688148476576" y="2.5074447073385526" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
<caption val="Function Center"/>
</element>
<command name="Point">
<input a0="Line[FuncCenter, FuncCenter + (0, 0, 1)]"/>
<output a0="FuncH"/>
</command>
<element type="point3d" label="FuncH">
<show object="true" label="true"/>
<condition showObject="showControls"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<ggbscript onUpdate="SetValue[h, z(FuncH)]"/>
<coords x="2.1442688148476576" y="2.5074447073385526" z="6.375749038369134" w="1.0"/>
<pointSize val="3"/>
<caption val="Function Height"/>
</element>
<command name="Segment">
<input a0="FuncH" a1="FuncCenter"/>
<output a0="segFuncControls"/>
</command>
<element type="segment3d" label="segFuncControls">
<show object="true" label="false"/>
<condition showObject="showControls"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="20" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="FlagPole"/>
<output a0="FlagPCon"/>
</command>
<element type="point3d" label="FlagPCon">
<show object="true" label="false"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<ggbscript val="RunClickScript[txtShowControls]"/>
<coords x="-2.138069506344078" y="5.735156497039938" z="4.876779273941657" w="1.0"/>
<pointSize val="3"/>
</element>
<expression label="txtShowControls" exp=""Show Controls""/>
<element type="text" label="txtShowControls">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="192" b="203" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="FlagPCon"/>
<labelOffset x="6" y="20"/>
<ggbscript val="SetValue[showControls, !showControls]"/>
</element>
<element type="boolean" label="showControls">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Sequence">
<input a0="Sequence[{Segment[(a1 + ((j - 1) * dx), b1 + ((k - 1) * dy), f(a1 + ((j - 1 / 2) * dx), b1 + ((k - 1 / 2) * dy))), (a1 + (j * dx), b1 + ((k - 1) * dy), f(a1 + ((j - 1 / 2) * dx), b1 + ((k - 1 / 2) * dy)))], Segment[(a1 + (j * dx), b1 + ((k - 1) * dy), f(a1 + ((j - 1 / 2) * dx), b1 + ((k - 1 / 2) * dy))), (a1 + (j * dx), b1 + (k * dy), f(a1 + ((j - 1 / 2) * dx), b1 + ((k - 1 / 2) * dy)))], Segment[(a1 + (j * dx), b1 + (k * dy), f(a1 + ((j - 1 / 2) * dx), b1 + ((k - 1 / 2) * dy))), (a1 + ((j - 1) * dx), b1 + (k * dy), f(a1 + ((j - 1 / 2) * dx), b1 + ((k - 1 / 2) * dy)))], Segment[(a1 + ((j - 1) * dx), b1 + (k * dy), f(a1 + ((j - 1 / 2) * dx), b1 + ((k - 1 / 2) * dy))), (a1 + ((j - 1) * dx), b1 + ((k - 1) * dy), f(a1 + ((j - 1 / 2) * dx), b1 + ((k - 1 / 2) * dy)))]}, k, 1, n]" a1="j" a2="1" a3="m"/>
<output a0="prismsTops"/>
</command>
<element type="list" label="prismsTops">
<show object="true" label="false"/>
<condition showObject="¬showPrism"/>
<objColor r="0" g="0" b="51" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
</construction>
</geogebra>