几何板应用：探究周长与几何变换
2020-11-16 07:37
本范例通过几何板演示周长的计算与几何变换。利用线段、圆和点等基础几何对象，结合旋转和平移操作，直观展示图形周界的构成与变化。通过动态交互，帮助学习者深入理解周长的概念及其在几何变换中的规律，适合中小学几何教学使用。
所属专题
几何板
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<condition showObject="SegType ≟ 1 ∨ SegType ≟ 2"/>
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<element type="text" label="TextLanguage">
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<element type="point" label="Seg09Po1">
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<input a0="Seg11Po1" a1="Length[Seg11]"/>
<output a0="Seg11Cir"/>
</command>
<element type="conic" label="Seg11Cir">
<show object="false" label="true" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-2" A3="0" A4="-1" A5="1"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="Seg12Po1" a1="Length[Seg12]"/>
<output a0="Seg12Cir"/>
</command>
<element type="conic" label="Seg12Cir">
<show object="false" label="true" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="1" A3="0" A4="-1" A5="2"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="Seg06Cir"/>
<output a0="Seg06Po2Rotate"/>
</command>
<element type="point" label="Seg06Po2Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="3" y="4" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Seg07Cir"/>
<output a0="Seg07Po2Rotate"/>
</command>
<element type="point" label="Seg07Po2Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="3" y="3" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Seg08Cir"/>
<output a0="Seg08Po2Rotate"/>
</command>
<element type="point" label="Seg08Po2Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="3" y="2" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Seg09Cir"/>
<output a0="Seg09Po2Rotate"/>
</command>
<element type="point" label="Seg09Po2Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="2.8601265042921575" y="1.7347988759040378" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Seg10Cir"/>
<output a0="Seg10Po2Rotate"/>
</command>
<element type="point" label="Seg10Po2Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="3" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Seg11Cir"/>
<output a0="Seg11Po2Rotate"/>
</command>
<element type="point" label="Seg11Po2Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="3" y="-1" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Seg12Cir"/>
<output a0="Seg12Po2Rotate"/>
</command>
<element type="point" label="Seg12Po2Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="2.2417581616059357" y="-3.567812701850909" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="Seg06Po1" a1="Seg06Po2Rotate"/>
<output a0="Seg06Rotate"/>
</command>
<element type="segment" label="Seg06Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="2"/>
<coords x="0" y="2" z="-8"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="Seg07Po1" a1="Seg07Po2Rotate"/>
<output a0="Seg07Rotate"/>
</command>
<element type="segment" label="Seg07Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="2"/>
<coords x="0" y="2" z="-6"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="Seg08Po1" a1="Seg08Po2Rotate"/>
<output a0="Seg08Rotate"/>
</command>
<element type="segment" label="Seg08Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="2"/>
<coords x="0" y="2" z="-4"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="Seg09Po1" a1="Seg09Po2Rotate"/>
<output a0="Seg09Rotate"/>
</command>
<element type="segment" label="Seg09Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="2"/>
<coords x="-0.7347988759040378" y="1.8601265042921575" z="-1.1253276283881197"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="Seg10Po1" a1="Seg10Po2Rotate"/>
<output a0="Seg10Rotate"/>
</command>
<element type="segment" label="Seg10Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="2"/>
<coords x="0" y="2" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="Seg11Po1" a1="Seg11Po2Rotate"/>
<output a0="Seg11Rotate"/>
</command>
<element type="segment" label="Seg11Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="2"/>
<coords x="0" y="2" z="2"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="Seg12Po1" a1="Seg12Po2Rotate"/>
<output a0="Seg12Rotate"/>
</command>
<element type="segment" label="Seg12Rotate">
<show object="true" label="false" ev="11"/>
<condition showObject="SegType ≟ 3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="2"/>
<coords x="1.567812701850909" y="1.2417581616059357" z="0.9157036213609624"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>