Hamid Naderi Yeganeh: Ellipse Art Construction
2019-02-22 01:42
This applet demonstrates the geometric construction of an ellipse inspired by Hamid Naderi Yeganeh's mathematical art. By defining focal coordinates and geometric points, it uses the Sequence command to precisely construct the ellipse. It highlights the beauty of conic sections and coordinate geometry, ideal for teaching analytic geometry and geometric constructions.
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.295.0" id="59f02fe7-b00e-477a-9979-402d318c832e" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1920" height="1040" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.23020833333333332" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1" size="400" window="1074,249,700,550" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="3,1" size="363" 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="3,1" 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="false" location="1,1" size="500" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1893" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="442" window="100,100,250,400" />
<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="1893" height="859"/>
<coordSystem xZero="886.2670366077385" yZero="464.57036791764034" scale="385.40684072700924" yscale="385.4068407270096"/>
<evSettings axes="false" 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="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<spreadsheetView>
<prefCellSize width="136" height="29"/>
<spreadsheetColumn id="0" width="70"/>
<spreadsheetColumn id="1" width="70"/>
<spreadsheetColumn id="2" width="70"/>
<spreadsheetColumn id="3" width="70"/>
<spreadsheetColumn id="4" width="70"/>
<spreadsheetColumn id="5" width="70"/>
<spreadsheetColumn id="6" width="70"/>
<spreadsheetColumn id="7" width="70"/>
<spreadsheetColumn id="8" width="70"/>
<spreadsheetColumn id="9" width="70"/>
<spreadsheetColumn id="10" width="70"/>
<spreadsheetColumn id="11" width="70"/>
<spreadsheetColumn id="12" width="70"/>
<spreadsheetColumn id="13" width="70"/>
<spreadsheetColumn id="14" width="70"/>
<spreadsheetColumn id="15" width="70"/>
<spreadsheetColumn id="17" width="70"/>
<spreadsheetColumn id="16" width="70"/>
<spreadsheetColumn id="19" width="70"/>
<spreadsheetColumn id="18" width="70"/>
<spreadsheetColumn id="21" width="70"/>
<spreadsheetColumn id="20" width="70"/>
<spreadsheetColumn id="23" width="70"/>
<spreadsheetColumn id="22" width="70"/>
<spreadsheetColumn id="25" width="70"/>
<spreadsheetColumn id="24" width="70"/>
<layout showFormulaBar="true" showGrid="true" showHScrollBar="true" showVScrollBar="true" showColumnHeader="true" showRowHeader="true" allowToolTips="true"/>
<spreadsheetCellFormat formatMap="0,0,a,4,b,15,f,0"/>
</spreadsheetView>
<kernel>
<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"/>
<construction title="" author="" date="">
<element type="numeric" label="a">
<value val="8000.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="8000" absoluteScreenLocation="true" width="200.0" x="235.0" y="92.0" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="100" speed="1" type="0" playing="false"/>
</element>
<command name="Sequence">
<input a0="((3 / 4 * sin(((2 * π) * k / 8000))) * cos(((6 * π) * k / 8000))) + (1 / 4 * sin(((28 * π) * k / 8000)))" a1="k" a2="1" a3="a"/>
<output a0="A"/>
</command>
<element type="list" label="A">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="1 / 18 + (1 / 20 * cos(((24 * π) * k / 8000)))" a1="k" a2="1" a3="a"/>
<output a0="C"/>
</command>
<element type="list" label="C">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="((3 / 4 * cos(((2 * π) * k / 8000))) * cos(((8 * π) * k / 8000))) + (1 / 4 * cos(((28 * π) * k / 8000)))" a1="k" a2="1" a3="a"/>
<output a0="B"/>
</command>
<element type="list" label="B">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="49 / 50 - (1 / 7 * sin(((10 * π) * k / 8000))^(4))" a1="k" a2="1" a3="a"/>
<output a0="D"/>
</command>
<element type="list" label="D">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Element[A, k] + (Element[C, k] * cos(((300 * π) * k / 8000)))" a1="k" a2="1" a3="a"/>
<output a0="F1x"/>
</command>
<element type="list" label="F1x">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Element[B, k] + (Element[C, k] * sin(((300 * π) * k / 8000)))" a1="k" a2="1" a3="a"/>
<output a0="F1y"/>
</command>
<element type="list" label="F1y">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Element[A, k] - (Element[C, k] * cos(((300 * π) * k / 8000)))" a1="k" a2="1" a3="a"/>
<output a0="F2x"/>
</command>
<element type="list" label="F2x">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Element[B, k] - (Element[C, k] * sin(((300 * π) * k / 8000)))" a1="k" a2="1" a3="a"/>
<output a0="F2y"/>
</command>
<element type="list" label="F2y">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="(Element[F1x, k], Element[F1y, k])" a1="k" a2="1" a3="a"/>
<output a0="F1"/>
</command>
<element type="list" label="F1">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="(Element[F2x, k], Element[F2y, k])" a1="k" a2="1" a3="a"/>
<output a0="F2"/>
</command>
<element type="list" label="F2">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Ellipse[Element[F1, k], Element[F2, k], Distance[Element[F1, k], Element[F2, k]] / ((2 * Element[D, k]))]" a1="k" a2="1" a3="a"/>
<output a0="列表1"/>
</command>
<element type="list" label="列表1">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="25"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
</construction>
</geogebra>