Height of Venus and Golden Ratio (Simple Version)
2019-06-09 14:28
This GeoGebra applet explores the golden ratio in the height of the Venus statue through geometric construction and length measurement. By using segments and points to construct key body parts, it calculates and displays the proportions at the navel and throat in real-time. The model intuitively demonstrates the practical application of the golden ratio in human aesthetics and geometric proportion
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.542.0" app="classic" platform="d" id="f8b34a0e-e91f-4aa6-985b-e0bf85985532" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1938" height="1048" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.15325077399380804" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="610,265,700,550" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<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="false" inframe="false" stylebar="true" location="1,1" size="782" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1607" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="297" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" 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" toolbar="0" 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" />
</views>
<toolbar show="true" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1607" height="832"/>
<coordSystem xZero="91.092106558167" yZero="671.6949539501477" scale="3.059677625571995" yscale="3.3037787065401285"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3" lockedAxesRatio="1.07978"/>
<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"/>
</euclidianView>
<algebraView>
<mode val="1"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2.0" max="2.0" step="1.0"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="a">
<value val="9.6"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="27" y="2"/>
<labelMode val="3"/>
<slider min="0" max="26" absoluteScreenLocation="true" width="200.0" x="279.0" y="301.0" fixed="true" horizontal="false" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
<caption val="控制肚脐高度"/>
</element>
<command name="Segment">
<input a0="(0, 105)" a1="(0, 0)"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="105.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-50" y="16"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="105.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="(0, 105 + a)"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-9.599999999999994" y="0.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="k" exp="((105 + g) / 2 * (sqrt(5) - 1))" />
<element type="numeric" label="k">
<value val="70.82669511073796"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="肚脐到脖子底部长度" exp="k - 26" />
<element type="numeric" label="肚脐到脖子底部长度">
<value val="44.82669511073796"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Point">
<input a0="g"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-58" y="1"/>
<labelMode val="3"/>
<fixed val="true"/>
<coords x="0.0" y="114.6" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
<caption val="肚脐"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="O"/>
</command>
<element type="point" label="O">
<show object="true" label="true" ev="4"/>
<objColor r="75" g="0" b="130" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="5" y="21"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="B" a1="(0, 105 + a + 肚脐到脖子底部长度)"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-44.82669511073797" y="0.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="h"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-33" y="14"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="158.94560440668522" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="c">
<value val="0.0"/>
<show object="true" label="true"/>
<objColor r="255" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="28" y="-1"/>
<labelMode val="3"/>
<slider min="0" max="20" absoluteScreenLocation="true" width="200.0" x="527.0" y="297.0" fixed="true" horizontal="false" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
<caption val="控制咽喉"/>
</element>
<command name="Segment">
<input a0="C" a1="(0, 105 + a + 肚脐到脖子底部长度 + c)"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.4810907040527468" y="0.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="i"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-59" y="9"/>
<labelMode val="3"/>
<fixed val="true"/>
<coords x="0.0" y="159.42669511073797" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
<caption val="咽喉"/>
</element>
<command name="Segment">
<input a0="C" a1="(0, 105 + a + 肚脐到脖子底部长度 + 26)"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-26.481090704052747" y="0.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="j"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="true" label="true" ev="4"/>
<objColor r="128" g="0" b="128" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-66" y="-4"/>
<labelMode val="3"/>
<fixed val="true"/>
<coords x="0.0" y="185.42669511073797" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
<caption val="头顶"/>
</element>
<command name="Length">
<input a0="Segment[E, B]"/>
<output a0="头顶到肚脐"/>
</command>
<element type="numeric" label="头顶到肚脐">
<value val="70.82669511073797"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="LaTeX">
<input a0="头顶到肚脐" a1="true" a2="true"/>
<output a0="text1"/>
</command>
<element type="text" label="text1">
<symbolic val="true" />
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.0" size="0" style="0"/>
<startPoint x="62.991351716895224" y="85.1541274225297" z="1.0"/>
</element>
<command name="Length">
<input a0="Segment[O, B]"/>
<output a0="肚脐到足底"/>
</command>
<element type="numeric" label="肚脐到足底">
<value val="114.6"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="LaTeX">
<input a0="肚脐到足底" a1="true" a2="true"/>
<output a0="text2"/>
</command>
<element type="text" label="text2">
<symbolic val="true" />
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.0" size="0" style="0"/>
<startPoint x="63.761464931272045" y="66.61210572084644" z="1.0"/>
</element>
<command name="Length">
<input a0="Segment[O, E]"/>
<output a0="身高"/>
</command>
<element type="numeric" label="身高">
<value val="185.42669511073797"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="LaTeX">
<input a0="身高" a1="true" a2="true"/>
<output a0="text3"/>
</command>
<element type="text" label="text3">
<symbolic val="true" />
<show object="true" label="true" ev="8"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.4" size="7" style="0"/>
<startPoint x="64.62148697621473" y="49.144758992558614" z="1.0"/>
</element>
<expression label="肚脐处比例" exp="头顶到肚脐 / 肚脐到足底" />
<element type="numeric" label="肚脐处比例">
<value val="0.6180339887498951"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="LaTeX">
<input a0="肚脐处比例" a1="true" a2="true"/>
<output a0="text4"/>
</command>
<element type="text" label="text4">
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.0" size="0" style="0"/>
<decimals val="5"/>
<startPoint x="63.14782588528652" y="108.66603214156714" z="1.0"/>
</element>
<expression label="咽喉处比例" exp="Length[Segment[E, D]] / Length[Segment[D, B]]" />
<element type="numeric" label="咽喉处比例">
<value val="0.5800115296425645"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="LaTeX">
<input a0="咽喉处比例" a1="true" a2="true"/>
<output a0="text5"/>
</command>
<element type="text" label="text5">
<show object="true" label="true" ev="8"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.0" size="0" style="0"/>
<decimals val="5"/>
<startPoint x="167.02482969526747" y="144.81749983958872" z="1.0"/>
</element>
<command name="LaTeX">
<input a0="肚脐到脖子底部长度" a1="true" a2="true"/>
<output a0="text7"/>
</command>
<element type="text" label="text7">
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.0" size="0" style="0"/>
<startPoint x="68.2300863300828" y="1.467055896703152" z="1.0"/>
</element>
</construction>
</geogebra>