Proof Without Words of the AM-GM Inequality
2020-08-19 09:00
This GeoGebra applet visually demonstrates the proof without words of the AM-GM inequality. By constructing geometric elements like semicircles, orthogonal lines, and segments, it creates line segments representing different means. Comparing their lengths clearly proves that the arithmetic mean is greater than or equal to the geometric mean without algebraic derivation, enhancing the understanding
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</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="t"/>
</command>
<element type="segment" label="t">
<show object="true" label="false" ev="4"/>
<condition showObject="1 ≤ N ≤ 3"/>
<objColor r="255" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<coords x="0.0" y="10.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>