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This video is a compilation of seven shorter videos that I have created showing various visual proofs without words of the famous AM-GM inequality, which states that the arithmetic mean of two numbers (a+b)/2 is greater than or equal to the geometric mean of the two numbers square root of a times b.
To see the original videos (in shorter form and sometimes with words/explanations), check the links below. Of course there are many other visual proofs of this amazing fact, but these are my favorite seven.
Let me know your favorite in the comments!
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Here are the original series videos (along with attribution; for more detailed attribution, see the original videos):
0:00 Introduction
0:05 Folding Proof : • Folding the AM-GM Ineq... and • Fold the AM-GM inequality (attribution: Yukio Kobayashi)
0:40 Circle with Triangles : • Mean Inequalities (vis... (attribution: Roger B. Nelsen)
1:07 Sliding Triangles: • AM-GM Inequality III (... (attribution: Claudi Alsina and Roger B. Nelsen)
1:52 Tangent Circles : • AM-GM Inequality IV (v... (attribution : Roland H. Eddy)
2:38 Eight Kites : • AM-GM Inequality VI (v... (attribution: Ayoub B. Ayoub)
3:27 Tatami : • Visual Proof of AM-GM ... and • AM-GM inequality visually (attribution: Doris Schattschneider)
4:05 Semicircle : • AM-GM Inequality II (v... and • AM-GM Inequality II (attribution: Charles D. Gallant)
4:49 Ending citation
If you like this inequality or others, you can check out my playlists of inequalities and AM-GM inequality:
Inequalities: • Inequalities
AM-GM : • AMGM Inequality
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