Ellipsograph (Trammel of Archimedes) Interactive Demo
2019-05-29 03:59
This applet demonstrates the Trammel of Archimedes. Users can adjust segment AB and point P via sliders, drawing the ellipse locus by dragging endpoints or using animation. It displays major and minor axis lengths in real-time, offering intuitive exploration of parametric equations and ellipse generation for coordinate geometry.
In collections
Conic Sections | GeoGebra Book Collection
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<element type="point" label="NowB">
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<command name="Polygon">
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<command name="If">
<input a0="a" a1="ff" a2="gg"/>
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<element type="ray" label="NowL">
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<element type="vector" label="VA">
<show object="false" label="true" ev="4"/>
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<command name="Intersect">
<input a0="Circle[(0, 0), 0.36]" a1="OrthogonalLine[(0, 0), VA]"/>
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<element type="point" label="V_1">
<show object="false" label="false"/>
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<element type="boolean" label="j">
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<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="橢圓規軌道Track of Ellipsograph"/>
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<show object="true" label="true"/>
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<checkbox fixed="true"/>
<caption val="橢圓資訊Information"/>
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<element type="boolean" label="ani">
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<show object="true" label="true"/>
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<checkbox fixed="true"/>
<ggbscript onUpdate="If(!ani,StartAnimation[false])
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<show object="true" label="false" ev="8"/>
<condition showObject="info ∧ NowA ≠ NowP ∧ NowB ≠ NowP"/>
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<expression label="text9" exp=""長軸長\text{major axis}:" + (LaTeX[(2 * If[r + ap ≟ pb, Distance[NowP, NowB], If[ap + pb ≟ r, If[ap > pb, ap, pb], Distance[NowP, NowA]]])]) + """ />
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<expression label="text12" exp=""橢圓方程式\text{Equation of Ellipse}:\\
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<expression label="text11" exp=""不是橢圓\hspace{2em}\text{Not an ellipse.}\\為" + (LaTeX[If[NowA ≟ NowP, "水平線段\hspace{1em}\text{A horizontal segment}", "鉛垂線段\hspace{1em}\text{A vertical segment}"]]) + "\\線段長:" + (LaTeX[(2 * r)]) + "\hspace{1em}\text{with length }" + (LaTeX[(2 * r)]) + "."" />
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<show object="true" label="false" ev="8"/>
<condition showObject="info ∧ (NowA ≟ NowP ∨ NowB ≟ NowP)"/>
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<expression label="text13" exp=""欲調整點A,\,B,\,P\,時，\hspace{1em}\text{If you want to drag}\\
先點擊該點一次，\hspace{2.8em}\text{point }A,\,B\,\text{or}\,P\,,\\
便可拖曳調整。\hspace{3.8em}\text{click it once first.}""/>
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<condition showObject="¬ani"/>
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