橡皮铅笔错觉的数学建模
2012-07-23 03:11
本范例通过数学方法对著名的“橡皮铅笔错觉”进行建模与演示。利用三角函数（正弦、余弦）、相似三角形及单位圆等概念，结合GeoGebra的轨迹与变换命令，模拟铅笔在特定频率和振幅下快速晃动时产生的视觉形变效果。通过调整振幅、相位差和手部运动参数，直观展示随机过程与几何变换如何共同作用形成这一经典的光学与运动错觉。
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我的第一个GeoGebra绘本
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<endStyle val="default"/>
<coords x="-2" y="0" z="10.2"/>
</element>
<element type="boolean" label="TFloci">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="800" y="175"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="loci at 3 pts"/>
</element>
<command name="Locus">
<input a0="F'" a1="θ"/>
<output a0="loc2"/>
</command>
<element type="locus" label="loc2">
<show object="true" label="false" ev="4"/>
<condition showObject="TFloci"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
</element>
</construction>
</geogebra>