Simulation of a Rolling Polygon
2020-01-06 03:23
This example demonstrates the dynamic process of a polygon rolling along a straight line. Using GeoGebra's rotation, centroid, and polygon commands, it accurately simulates the geometric transformations of an arbitrary polygon during rolling. Combined with integral calculus and coordinate geometry, it explores the locus of relevant points and the swept area, serving as an intuitive teaching tool f
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<value val="0.18534794999569476"/>
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
</element>
<command name="Rotate">
<input a0="Polygon[Translate[A', (0, m(x(l1(n))) - P)], Translate[B', (0, m(x(l1(n))) - P)], Translate[C', (0, m(x(l1(n))) - P)], Translate[D', (0, m(x(l1(n))) - P)], Translate[E', (0, m(x(l1(n))) - P)], Translate[F', (0, m(x(l1(n))) - P)]]" a1="(-α)" a2="l1(n)"/>
<output a0="p3"/>
</command>
<element type="polygon" label="p3">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="96" g="96" b="96" alpha="0.28999999165534973"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Integral">
<input a0="m" a1="-8" a2="8"/>
<output a0="o"/>
</command>
<element type="numeric" label="o">
<value val="24.0"/>
<symbolic val="true" />
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.10000000149011612" fillType="6" hatchAngle="0" hatchDistance="20"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
</element>
</construction>
</geogebra>