Sectioning and Partitioning a Cube
2020-04-18 22:52
This applet demonstrates how to section and partition a cube using GeoGebra. By constructing orthogonal planes and intersecting them with the cube, various cross-sectional polygons are generated. Combined with geometric transformations like translation, it visually displays the separated parts of the cube and their spatial geometric properties. This model helps in deeply understanding cross-sectio
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<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Zip">
<input a0="KeepIf[Angle[OrthogonalVector[s], Vector[R, p]] ≥ π / 2 ∧ p ∈ q, p, l2]" a1="q" a2="l3"/>
<output a0="l7"/>
</command>
<element type="list" label="l7">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="8"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Zip">
<input a0="KeepIf[Angle[OrthogonalVector[s], Vector[R, p]] ≤ π / 2 ∧ p ∈ q, p, l2]" a1="q" a2="l3"/>
<output a0="l5"/>
</command>
<element type="list" label="l5">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="RemoveUndefined">
<input a0="Zip[Polygon[Append[Element[q, 1], Sort[Take[q, 2], Zip[Angle[Element[q, 2], Element[q, 1], p], p, Take[q, 2]]]]], q, l5]"/>
<output a0="l6"/>
</command>
<element type="list" label="l6">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<element type="numeric" label="c">
<value val="0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="200" x="116" y="236" fixed="false" horizontal="false" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.001" speed="1" type="0" playing="false"/>
</element>
<command name="Translate">
<input a0="l6" a1="Vector[(c * OrthogonalVector[s])]"/>
<output a0="l6'"/>
</command>
<element type="list" label="l6'">
<show object="true" label="false" ev="5"/>
<objColor r="0" g="100" b="0" alpha="0.800000011920929"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="RemoveUndefined">
<input a0="Zip[Polygon[Append[Element[q, 1], Sort[Take[q, 2], Zip[Angle[Element[q, 2], Element[q, 1], p], p, Take[q, 2]]]]], q, l7]"/>
<output a0="l8"/>
</command>
<element type="list" label="l8">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Translate">
<input a0="l8" a1="Vector[((-c) * OrthogonalVector[s])]"/>
<output a0="l8'"/>
</command>
<element type="list" label="l8'">
<show object="true" label="true" ev="5"/>
<objColor r="255" g="127" b="0" alpha="0.800000011920929"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
</construction>
</geogebra>