Hamid Naderi Yeganeh: Ellipse Art Construction
2019-02-22 02:08
This example demonstrates an ellipse art construction inspired by Hamid Naderi Yeganeh. Using the Sequence command with focal points and polynomial functions, it constructs ellipses and related figures. It illustrates ellipse foci properties and showcases parametric equations and sequence lists for mathematical art, integrating coordinate geometry and graphing.
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<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
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<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="a">
<value val="5600.0"/>
<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="5600" absoluteScreenLocation="true" width="200.0" x="235.0" y="92.0" fixed="true" horizontal="true" showAlgebra="true"/>
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<command name="Sequence">
<input a0="cos(((28 * π) * k / 5600))^(3)" a1="k" a2="1" a3="a"/>
<output a0="A"/>
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<lineStyle thickness="2" type="0" typeHidden="1"/>
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<pointStyle val="-1"/>
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<command name="Sequence">
<input a0="1 / 70 + 1 / 6 + (1 / 6 * sin(((28 * π) * k / 5600)))" a1="k" a2="1" a3="a"/>
<output a0="C"/>
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<lineStyle thickness="2" type="0" typeHidden="1"/>
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<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="sin(((28 * π) * k / 5600)) + (1 / 4 * cos(((14 * π) * k / 5600) - (7 * π / 4))^(18))" a1="k" a2="1" a3="a"/>
<output a0="B"/>
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<command name="Sequence">
<input a0="399 / 400 - (1 / 6 * sin(((28 * π) * k / 5600))^(8))" a1="k" a2="1" a3="a"/>
<output a0="D"/>
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<pointStyle val="-1"/>
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<command name="Sequence">
<input a0="Element[A, k] + (Element[C, k] * cos(((44 * π) * k / 5600)))" a1="k" a2="1" a3="a"/>
<output a0="F1x"/>
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<command name="Sequence">
<input a0="Element[B, k] + (Element[C, k] * sin(((44 * π) * k / 5600)))" a1="k" a2="1" a3="a"/>
<output a0="F1y"/>
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<input a0="Element[A, k] - (Element[C, k] * cos(((44 * π) * k / 5600)))" a1="k" a2="1" a3="a"/>
<output a0="F2x"/>
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<command name="Sequence">
<input a0="Element[B, k] - (Element[C, k] * sin(((44 * π) * k / 5600)))" a1="k" a2="1" a3="a"/>
<output a0="F2y"/>
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<pointStyle val="-1"/>
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<command name="Sequence">
<input a0="(Element[F1x, k], Element[F1y, k])" a1="k" a2="1" a3="a"/>
<output a0="F1"/>
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<command name="Sequence">
<input a0="(Element[F2x, k], Element[F2y, k])" a1="k" a2="1" a3="a"/>
<output a0="F2"/>
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<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>
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