祖暅原理（卡瓦列里原理）三维演示
2018-07-30 16:26
本GeoGebra范例直观演示了祖暅原理（卡瓦列里原理）。通过构建两个等高且在任意相同高度处截面积均相等的立体图形（如棱柱与曲面体），动态展示它们体积必然相等的几何本质。该原理是微积分中利用截面面积计算立体体积的重要基础，非常适合立体几何与积分学的可视化教学。
所属专题
我的第一个GeoGebra互动绘本
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.481.0" app="classic" platform="w" id="acea55c6-9980-456e-9748-926548b03e53" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="875" height="566" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.7985865724381626" orientation="0" />
</panes>
<views>
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1,1,1" size="400" window="960,520,974,723" />
<view id="1" visible="false" inframe="false" stylebar="true" location="0,3" size="351" window="94,192,600,750" />
<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="false" stylebar="true" location="0,3" size="257" window="1285,223,400,632" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="16" visible="true" inframe="false" stylebar="false" location="2" size="104" window="426,259,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="true" location="1" size="150" 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="150" 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="false" location="0" size="452" window="100,100,600,400" />
</views>
<toolbar show="false" 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="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="598" height="438"/>
<coordSystem xZero="245.0485112319141" yZero="352.1456559465359" scale="66.90445495258949" yscale="66.90445495258928"/>
<evSettings axes="true" grid="false" 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="0"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="873" height="104"/>
<coordSystem xZero="204" yZero="74.99999999999994" scale="50" yscale="49.99999999999996"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="2" 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="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="0.1" distY="0.1" distTheta="0.5235987755982988"/>
</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="0.20675098437972167" yZero="-1.98967817647884" zZero="-1.1974740672825368" scale="77.42318547099732" xAngle="10" zAngle="-77.3614918393321"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="2" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<plate show="false"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="2"/>
<projection type="0"/>
</euclidianView3D>
<construction title="Cavalieri's Principle" author="" date="">
<expression label="A" exp="(1.5, -1, 0)" type="point"/>
<element type="point3d" label="A">
<show object="false" label="false" ev="4"/>
<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="1.5" y="-1" z="0" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="B">
<show object="false" label="false" ev="4"/>
<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="4" y="-1" z="0" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="C">
<show object="false" label="false" ev="4"/>
<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="4" y="2" z="0" w="1"/>
<pointSize val="3"/>
</element>
<expression label="C1" exp="A + C - B" type="point" />
<element type="point3d" label="C1">
<show object="false" label="true" ev="7"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="1.5" y="2" z="0" w="1"/>
<pointSize val="3"/>
</element>
<command name="Polygon">
<input a0="A" a1="B" a2="C" a3="C1"/>
<output a0="poly1" a1="b" a2="c" a3="g_1" a4="h_1"/>
</command>
<element type="polygon3d" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="true" label="false" ev="5"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="segment3d" label="b">
<show object="true" label="false" ev="7"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="c">
<show object="true" label="false" ev="5"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="g_1">
<show object="true" label="false" ev="7"/>
<objColor r="255" g="204" b="51" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="h_1">
<show object="true" label="false" ev="5"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Prism">
<input a0="poly1" a1="2.972510101050426"/>
<output a0="d" a1="D" a2="E" a3="F" a4="F1" a5="faceBCFE" a6="faceACFD" a7="faceDEF" a8="edgeAD" a9="edgeBE" a10="edgeCF" a11="edgeDE" a12="edgeEF" a13="edgeDF" a14="edge1" a15="edge2" a16="edge3" a17="edge4"/>
</command>
<element type="polyhedron" label="d">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="153" g="51" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="point3d" label="D">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.5" y="-1" z="2.972510101050426" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="E">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4" y="-1" z="2.972510101050426" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="F">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4" y="2" z="2.972510101050426" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="F1">
<show object="false" label="true" ev="4"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.5" y="2" z="2.972510101050426" w="1"/>
<pointSize val="3"/>
</element>
<element type="polygon3d" label="faceBCFE">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="false" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceACFD">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="false" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceDEF">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="false" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="edgeAD">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="false" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="edgeBE">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="false" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="segment3d" label="edgeCF">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeDE">
<show object="false" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeEF">
<show object="false" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeDF">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge1">
<show object="false" label="false" ev="7"/>
<objColor r="153" g="51" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge2">
<show object="false" label="false" ev="7"/>
<objColor r="153" g="51" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge3">
<show object="false" label="false" ev="7"/>
<objColor r="255" g="204" b="51" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge4">
<show object="false" label="false" ev="7"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="polygon3d" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="true" label="false" ev="5"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="segment3d" label="b">
<show object="true" label="false" ev="7"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="h_1">
<show object="true" label="false" ev="5"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="c">
<show object="true" label="false" ev="5"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="g_1">
<show object="true" label="false" ev="7"/>
<objColor r="255" g="204" b="51" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Height">
<input a0="d"/>
<output a0="h"/>
</command>
<element type="numeric" label="h">
<value val="2.972510101050426"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<element type="point3d" label="G">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-5" y="0" z="0" w="1"/>
<pointSize val="5"/>
</element>
<command name="Segment">
<input a0="G" a1="G + (0, 0, h)"/>
<output a0="l"/>
</command>
<element type="segment3d" label="l">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="l"/>
<output a0="H"/>
</command>
<element type="point3d" label="H">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-5" y="0" z="1.6968451464859289" w="1"/>
<pointSize val="5"/>
</element>
<expression label="h'" exp="z(H)" />
<element type="numeric" label="h'">
<value val="1.6968451464859289"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="Q1" exp="C1 + (0, 0, h')" type="point" />
<element type="point3d" label="Q1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="1.5" y="2" z="1.6968451464859289" w="1"/>
<pointSize val="3"/>
</element>
<expression label="Q" exp="C + (0, 0, h')" type="point" />
<element type="point3d" label="Q">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4" y="2" z="1.6968451464859289" w="1"/>
<pointSize val="3"/>
</element>
<expression label="P" exp="B + (0, 0, h')" type="point" />
<element type="point3d" label="P">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4" y="-1" z="1.6968451464859289" w="1"/>
<pointSize val="3"/>
</element>
<expression label="O" exp="A + (0, 0, h')" type="point" />
<element type="point3d" label="O">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.5" y="-1" z="1.6968451464859289" w="1"/>
<pointSize val="3"/>
</element>
<expression label="W" exp="(-4.5, 0, 0)" type="point"/>
<element type="point3d" label="W">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="-4.5" y="0" z="0" w="1"/>
<pointSize val="5"/>
</element>
<expression label="C'" exp="C + W" type="point" />
<element type="point3d" label="C'">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.5" y="2" z="0" w="1"/>
<pointSize val="3"/>
</element>
<expression label="x3" exp="x(C')" />
<element type="numeric" label="x3">
<value val="-0.5"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="y3" exp="y(C')" />
<element type="numeric" label="y3">
<value val="2"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="B'" exp="B + W" type="point" />
<element type="point3d" label="B'">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.5" y="-1" z="0" w="1"/>
<pointSize val="3"/>
</element>
<expression label="x2" exp="x(B')" />
<element type="numeric" label="x2">
<value val="-0.5"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="y2" exp="y(B')" />
<element type="numeric" label="y2">
<value val="-1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="A'" exp="A + W" type="point" />
<element type="point3d" label="A'">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3" y="-1" z="0" w="1"/>
<pointSize val="3"/>
</element>
<expression label="x1" exp="x(A')" />
<element type="numeric" label="x1">
<value val="-3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="y1" exp="y(A')" />
<element type="numeric" label="y1">
<value val="-1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="C1'" exp="C1 + W" type="point" />
<element type="point3d" label="C1'">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="-3" y="2" z="0" w="1"/>
<pointSize val="3"/>
</element>
<expression label="x4" exp="x(C1')" />
<element type="numeric" label="x4">
<value val="-3"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="y4" exp="y(C1')" />
<element type="numeric" label="y4">
<value val="2"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<element type="numeric" label="t">
<value val="1"/>
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="200" x="279" y="35" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.05" speed="1" type="0" playing="false"/>
</element>
<command name="If">
<input a0="t < 0.5" a1="0" a2="(2 * (t - 0.5))"/>
<output a0="t2"/>
</command>
<element type="numeric" label="t2">
<value val="1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="If">
<input a0="t < 0.5" a1="(2 * t)" a2="1"/>
<output a0="t1"/>
</command>
<element type="numeric" label="t1">
<value val="1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="f" exp="f(s) = (((-0.5 * t1) * (1 - t2)) * s) - ((0.3 * t2) * sin(((2 * π) * s / h)))" />
<element type="function" label="f">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
</element>
<expression label="N1" exp="(f(h') + x4, y4, h')" type="point" />
<element type="point3d" label="N1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="-2.87082532412934" y="2" z="1.6968451464859289" w="1"/>
<pointSize val="3"/>
</element>
<expression label="N" exp="(f(h') + x3, y3, h')" type="point" />
<element type="point3d" label="N">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.3708253241293402" y="2" z="1.6968451464859289" w="1"/>
<pointSize val="3"/>
</element>
<expression label="M" exp="(f(h') + x2, y2, h')" type="point" />
<element type="point3d" label="M">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.3708253241293402" y="-1" z="1.6968451464859289" w="1"/>
<pointSize val="3"/>
</element>
<expression label="L" exp="(f(h') + x1, y1, h')" type="point" />
<element type="point3d" label="L">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.87082532412934" y="-1" z="1.6968451464859289" w="1"/>
<pointSize val="3"/>
</element>
<expression label="K1" exp="(f(h) + x4, y4, h)" type="point" />
<element type="point3d" label="K1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="-3" y="2" z="2.972510101050426" w="1"/>
<pointSize val="3"/>
</element>
<expression label="I" exp="(f(h) + x1, y1, h)" type="point" />
<element type="point3d" label="I">
<show object="false" label="true" ev="7"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3" y="-1" z="2.972510101050426" w="1"/>
<pointSize val="3"/>
</element>
<expression label="J" exp="(f(h) + x2, y2, h)" type="point" />
<element type="point3d" label="J">
<show object="false" label="true" ev="7"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.49999999999999994" y="-1" z="2.972510101050426" w="1"/>
<pointSize val="3"/>
</element>
<expression label="K" exp="(f(h) + x3, y3, h)" type="point" />
<element type="point3d" label="K">
<show object="false" label="true" ev="7"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.49999999999999994" y="2" z="2.972510101050426" w="1"/>
<pointSize val="3"/>
</element>
<expression label="w" exp="30"/>
<element type="numeric" label="w">
<value val="30"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="1"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Polygon">
<input a0="C'" a1="C1'" a2="A'" a3="B'"/>
<output a0="poly2" a1="m_1" a2="n_1" a3="p_1" a4="q_1"/>
</command>
<element type="polygon3d" label="poly2">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="m_1">
<show object="true" label="false" ev="7"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="n_1">
<show object="true" label="false" ev="5"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="p_1">
<show object="true" label="false" ev="7"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="q_1">
<show object="true" label="false" ev="5"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="CurveCartesian">
<input a0="f(u) + x1" a1="y1" a2="u" a3="u" a4="0" a5="h"/>
<output a0="e"/>
</command>
<element type="curvecartesian3d" label="e">
<show object="false" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
</element>
<command name="CurveCartesian">
<input a0="f(u) + x2" a1="y2" a2="u" a3="u" a4="0" a5="h"/>
<output a0="g"/>
</command>
<element type="curvecartesian3d" label="g">
<show object="false" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
</element>
<command name="CurveCartesian">
<input a0="f(u) + x3" a1="y3" a2="u" a3="u" a4="0" a5="h"/>
<output a0="i"/>
</command>
<element type="curvecartesian3d" label="i">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
</element>
<command name="Surface">
<input a0="(u * (f(v) + x1)) + ((1 - u) * (f(v) + x2))" a1="(u * y1) + ((1 - u) * y2)" a2="v" a3="u" a4="0" a5="1" a6="v" a7="0" a8="h"/>
<output a0="j"/>
</command>
<element type="surfacecartesian3d" label="j">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<command name="Surface">
<input a0="(u * (f(v) + x2)) + ((1 - u) * (f(v) + x3))" a1="(u * y2) + ((1 - u) * y3)" a2="v" a3="u" a4="0" a5="1" a6="v" a7="0" a8="h"/>
<output a0="k"/>
</command>
<element type="surfacecartesian3d" label="k">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<command name="Polygon">
<input a0="L" a1="M" a2="N" a3="N1"/>
<output a0="poly4" a1="m" a2="n" a3="l_1" a4="s_1"/>
</command>
<element type="polygon3d" label="poly4">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="m">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="n">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="l_1">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="s_1">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="O" a1="P" a2="Q" a3="Q1"/>
<output a0="poly5" a1="p" a2="q" a3="t_1" a4="g_2"/>
</command>
<element type="polygon3d" label="poly5">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="p">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="q">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="t_1">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="g_2">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="I" a1="J" a2="K" a3="K1"/>
<output a0="poly3" a1="i_1" a2="j_1" a3="k_1" a4="r_1"/>
</command>
<element type="polygon3d" label="poly3">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="i_1">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="j_1">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="k_1">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="r_1">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="(-7, -7, h')" a1="(7, -7, h')" a2="(7, 7, h')" a3="(-7, 7, h')"/>
<output a0="poly6" a1="r" a2="s" a3="b_1" a4="c_1"/>
</command>
<element type="polygon3d" label="poly6">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="99" g="219" b="219" alpha="0.20000000298023224"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="segment3d" label="r">
<show object="false" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="s">
<show object="false" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="b_1">
<show object="false" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="c_1">
<show object="false" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="d_1"/>
</command>
<element type="segment3d" label="d_1">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="C"/>
<output a0="e_1"/>
</command>
<element type="segment3d" label="e_1">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="δ" exp="h / w" />
<element type="numeric" label="δ">
<value val="0.0990836700350142"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<element type="boolean" label="o1">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="514" y="15"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[o1, true] SetValue[o2, false]"/>
<caption val="Stacks of Slabs"/>
</element>
<element type="boolean" label="o2">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="709" y="15"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[o1, false] SetValue[o2, true]"/>
<caption val="Solids"/>
</element>
<expression label="text2" exp=""Change the shape of the solid""/>
<element type="text" label="text2">
<show object="true" label="false" ev="11"/>
<condition showObject="o2"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<absoluteScreenLocation x="5" y="39"/>
</element>
<expression label="text3" exp=""Move the stack of slabs""/>
<element type="text" label="text3">
<show object="true" label="false" ev="43"/>
<condition showObject="o1"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<absoluteScreenLocation x="50" y="39"/>
</element>
<expression label="text1" exp=""" + (If[o2, "If two solids have equal cross-section areas at the same height, they have equal volumes.", "Two stacks of equal slabs always have the same volumes."]) + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<absoluteScreenLocation x="5" y="26"/>
</element>
<command name="Sequence">
<input a0="Prism[Polygon[A + (0, 0, (i * δ)), B + (0, 0, (i * δ)), C + (0, 0, (i * δ)), C1 + (0, 0, (i * δ))], δ]" a1="i" a2="0" a3="w - 1"/>
<output a0="list1"/>
</command>
<element type="list" label="list1">
<show object="true" label="true" ev="4"/>
<condition showObject="o1"/>
<objColor r="255" g="204" b="51" alpha="1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Prism[Polygon[(f((i * δ)) + x1, y1, (i * δ)), (f((i * δ)) + x2, y2, (i * δ)), (f((i * δ)) + x3, y3, (i * δ)), (f((i * δ)) + x4, y4, (i * δ))], δ]" a1="i" a2="0" a3="w - 1"/>
<output a0="list2"/>
</command>
<element type="list" label="list2">
<show object="true" label="false" ev="4"/>
<condition showObject="o1"/>
<objColor r="255" g="204" b="51" alpha="1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Prism[Polygon[(f((i * δ)) + x1, y1, (i * δ)), (f((i * δ)) + x2, y2, (i * δ)), (f((i * δ)) + x3, y3, (i * δ)), (f((i * δ)) + x4, y4, (i * δ))], δ]" a1="i" a2="0" a3="w - 1"/>
<output a0="list2'"/>
</command>
<element type="list" label="list2'">
<show object="true" label="false" ev="4"/>
<condition showObject="o1"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Segment">
<input a0="C" a1="C1"/>
<output a0="f_1"/>
</command>
<element type="segment3d" label="f_1">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="CurveCartesian">
<input a0="f(u) + x4" a1="y4" a2="u" a3="u" a4="0" a5="h"/>
<output a0="u"/>
</command>
<element type="curvecartesian3d" label="u">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
</element>
<command name="Surface">
<input a0="(u * (f(v) + x4)) + ((1 - u) * (f(v) + x3))" a1="(u * y4) + ((1 - u) * y3)" a2="v" a3="u" a4="0" a5="1" a6="v" a7="0" a8="h"/>
<output a0="a"/>
</command>
<element type="surfacecartesian3d" label="a">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<command name="Surface">
<input a0="(u * (f(v) + x4)) + ((1 - u) * (f(v) + x1))" a1="(u * y4) + ((1 - u) * y1)" a2="v" a3="u" a4="0" a5="1" a6="v" a7="0" a8="h"/>
<output a0="v"/>
</command>
<element type="surfacecartesian3d" label="v">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<command name="Polygon">
<input a0="D" a1="E" a2="F" a3="F1"/>
<output a0="q1" a1="d_2" a2="e_2" a3="f_2" a4="f1"/>
</command>
<element type="polygon3d" label="q1">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="d_2">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="e_2">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="f_2">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="f1">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="A" a1="D" a2="F1" a3="C1"/>
<output a0="q2" a1="a_1" a2="d_3" a3="f1_1" a4="c1"/>
</command>
<element type="polygon3d" label="q2">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="204" b="51" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="a_1">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="d_3">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="204" b="51" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="f1_1">
<show object="true" label="false" ev="4"/>
<condition showObject="o2"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="c1">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="204" b="51" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="list1'" exp="list1" />
<element type="list" label="list1'">
<show object="true" label="false" ev="4"/>
<condition showObject="o1"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
</construction>
</geogebra>