棱锥侧面间的二面角 1
2016-09-16 12:14
本GeoGebra范例演示了如何计算和可视化四棱锥相邻侧面之间的二面角。通过构建棱锥的顶点、底面多边形及侧棱，利用球面、交线和中点等几何构造方法，精确作出二面角的平面角。该模型有助于直观理解立体几何中面面角的定义与求解过程，适用于立体几何教学。
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<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
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<output a0="β"/>
</command>
<element type="angle3d" label="β">
<angleStyle val="1"/>
<value val="1.6698593718618784"/>
<show object="true" label="true" ev="4"/>
<condition showObject="q"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
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<labelOffset x="-61" y="-26"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
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</element>
<command name="Polygon">
<input a0="C" a1="A" a2="K"/>
<output a0="poly1" a1="k_1" a2="c_1" a3="a_1"/>
</command>
<element type="polygon3d" label="poly1">
<lineStyle thickness="0" type="0" typeHidden="1"/>
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<condition showObject="q"/>
<objColor r="255" g="255" b="0" alpha="0.45"/>
<layer val="0"/>
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</element>
<element type="segment3d" label="k_1">
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<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="c_1">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
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<labelMode val="0"/>
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<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="a_1">
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<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
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<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="K"/>
<output a0="p"/>
</command>
<element type="segment3d" label="p">
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<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
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<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="B" a1="K" a2="A"/>
<output a0="γ"/>
</command>
<element type="angle3d" label="γ">
<angleStyle val="1"/>
<value val="1.5707963267948963"/>
<show object="true" label="false" ev="4"/>
<condition showObject="o"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
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<lineStyle thickness="2" type="0" typeHidden="2"/>
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</element>
<command name="Angle">
<input a0="B" a1="K" a2="C"/>
<output a0="δ"/>
</command>
<element type="angle3d" label="δ">
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<condition showObject="o"/>
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</element>
<element type="boolean" label="o">
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<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
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<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="Hint"/>
</element>
<element type="boolean" label="q">
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<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
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<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="Answer"/>
</element>
</construction>
</geogebra>