Amoeba Curve Construction

2016-06-19 14:38

This applet constructs a complex geometric shape resembling an amoeba using the Cartesian curve command. By integrating fundamental geometric and algebraic elements such as ellipses, isosceles triangles, and linear functions, it demonstrates the generation of specific curves. This example visually illustrates curve plotting in analytic geometry and is ideal for exploring function graphing and geom

#coordinate-geometry #graphing #geometry-construction #parametric

<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.240.0" id="386F18A2-60C2-4092-A345-0B7E54355A06"  xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
	<window width="1280" height="777" />
	<perspectives>
<perspective id="tmp">
	<panes>
		<pane location="" divider="0.23359375" orientation="1" />
	</panes>
	<views>
		<view id="4" toolbar="0 || 2020 , 2021 , 2022 || 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 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
		<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="383" window="100,100,700,550" />
		<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="972" window="100,100,600,400" />
		<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="299" window="100,100,250,400" />
		<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="300" window="50,50,500,500" />
		<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="300" window="50,50,500,500" />
		<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
		<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="900" window="50,50,500,500" />
	</views>
	<toolbar show="true" items="0 | 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 | 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="algebra" />
	<dockBar show="false" east="false" />
</perspective>
	</perspectives>
	<labelingStyle  val="0"/>
	<font  size="12"/>
</gui>
<euclidianView>
	<size  width="972" height="650"/>
	<coordSystem xZero="404.00000000000006" yZero="335.0" scale="50.00000000000001" yscale="50.0"/>
	<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>
<algebraView>
	<mode val="3"/>
</algebraView>
<kernel>
	<continuous val="false"/>
	<usePathAndRegionParameters val="true"/>
	<decimals val="2"/>
	<angleUnit val="degree"/>
	<algebraStyle val="0" spreadsheet="0"/>
	<coordStyle val="0"/>
	<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="c">
	<value val="-3.0"/>
	<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="50.0" fixed="true" horizontal="true" showAlgebra="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="-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="90.0" fixed="true" horizontal="true" showAlgebra="true"/>
	<lineStyle thickness="10" type="0" typeHidden="1"/>
	<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="d">
	<value val="1.31"/>
	<show object="true" label="true"/>
	<objColor r="0" g="0" b="0" alpha="0.1"/>
	<layer val="0"/>
	<labelMode val="1"/>
	<slider min="0.01" max="5" absoluteScreenLocation="true" width="200.0" x="30.0" y="130.0" fixed="true" horizontal="true" showAlgebra="true"/>
	<lineStyle thickness="10" type="0" typeHidden="1"/>
	<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<command name="CurveCartesian">
	<input a0="log(abs((d * t)))" a1="log(abs(ℯ^(((-(5 / 7)) * c)) - (t * ℯ^(((-(8 / 21)) * b)))))" a2="t" a3="-100" a4="100"/>
	<output a0="a"/>
</command>
<element type="curvecartesian" label="a">
	<show object="true" label="true"/>
	<objColor r="0" g="0" b="0" alpha="1.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
</construction>
</geogebra>

<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.240.0" id="386F18A2-60C2-4092-A345-0B7E54355A06"  xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
	<window width="1280" height="777" />
	<perspectives>
<perspective id="tmp">
	<panes>
		<pane location="" divider="0.23359375" orientation="1" />
	</panes>
	<views>
		<view id="4" toolbar="0 || 2020 , 2021 , 2022 || 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 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
		<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="383" window="100,100,700,550" />
		<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="972" window="100,100,600,400" />
		<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="299" window="100,100,250,400" />
		<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="300" window="50,50,500,500" />
		<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="300" window="50,50,500,500" />
		<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
		<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="900" window="50,50,500,500" />
	</views>
	<toolbar show="true" items="0 | 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 | 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="algebra" />
	<dockBar show="false" east="false" />
</perspective>
	</perspectives>
	<labelingStyle  val="0"/>
	<font  size="12"/>
</gui>
<euclidianView>
	<size  width="972" height="650"/>
	<coordSystem xZero="404.00000000000006" yZero="335.0" scale="50.00000000000001" yscale="50.0"/>
	<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>
<algebraView>
	<mode val="3"/>
</algebraView>
<kernel>
	<continuous val="false"/>
	<usePathAndRegionParameters val="true"/>
	<decimals val="2"/>
	<angleUnit val="degree"/>
	<algebraStyle val="0" spreadsheet="0"/>
	<coordStyle val="0"/>
	<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="c">
	<value val="-3.0"/>
	<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="50.0" fixed="true" horizontal="true" showAlgebra="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="-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="90.0" fixed="true" horizontal="true" showAlgebra="true"/>
	<lineStyle thickness="10" type="0" typeHidden="1"/>
	<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="d">
	<value val="1.31"/>
	<show object="true" label="true"/>
	<objColor r="0" g="0" b="0" alpha="0.1"/>
	<layer val="0"/>
	<labelMode val="1"/>
	<slider min="0.01" max="5" absoluteScreenLocation="true" width="200.0" x="30.0" y="130.0" fixed="true" horizontal="true" showAlgebra="true"/>
	<lineStyle thickness="10" type="0" typeHidden="1"/>
	<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<command name="CurveCartesian">
	<input a0="log(abs((d * t)))" a1="log(abs(ℯ^(((-(5 / 7)) * c)) - (t * ℯ^(((-(8 / 21)) * b)))))" a2="t" a3="-100" a4="100"/>
	<output a0="a"/>
</command>
<element type="curvecartesian" label="a">
	<show object="true" label="true"/>
	<objColor r="0" g="0" b="0" alpha="1.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
</construction>
</geogebra>