Geometric Visualization of the AM-GM Inequality
2018-11-27 03:27
This applet provides a geometric visualization of the Arithmetic Mean-Geometric Mean (AM-GM) inequality. By constructing polygons and utilizing intersection points, it intuitively demonstrates the relationship between the arithmetic and geometric means of non-negative real numbers. This interactive model helps learners understand the geometric essence of this classic algebraic inequality and its a
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<expression label="text5" exp=""正方形面積={(\frac{a+b}{2})}^{2}""/>
<element type="text" label="text5">
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<condition showObject="-0.3 ≤ f"/>
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<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="7" style="1"/>
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<expression label="text6" exp=""正方形面積比長方形面積大""/>
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<condition showObject="2.2 ≤ f"/>
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<labelMode val="0"/>
<algebra labelVisible="false"/> <font serif="true" sizeM="2" size="16" style="1"/>
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<expression label="text7" exp=""ab≤{(\frac{a+b}{2})}^{2}""/>
<element type="text" label="text7">
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<condition showObject="2.4 ≤ f"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="7" style="1"/>
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<expression label="text8" exp=""\sqrt{ab}≤\frac{a+b}{2}""/>
<element type="text" label="text8">
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<condition showObject="2.5 ≤ f"/>
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<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="7" style="1"/>
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<element type="button" label="button1">
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<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(on,!on)
StartAnimation(f)
StartAnimation(on)
SetValue(f,If(f≟2.5,-1,f))
SetCaption(button1,If(on≟true,"暫停動畫","開始動畫"))"/>
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<element type="boolean" label="on">
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<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
</construction>
</geogebra>