Arithmetic Mean-Geometric Mean Visual Proof Compilation

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 Inequality V (quick...   and    • Fold the AM-GM inequality   (attribution: Yukio Kobayashi)
0:40 Circle with Triangles :    • Mean Inequalities (visual proof of AM...   (attribution: Roger B. Nelsen)
1:07 Sliding Triangles:    • AM-GM Inequality III (visual proof)   (attribution: Claudi Alsina and Roger B. Nelsen)
1:52 Tangent Circles :    • AM-GM Inequality IV (visual proof)   (attribution : Roland H. Eddy)
2:38 Eight Kites :    • AM-GM Inequality VI (visual proof)   (attribution: Ayoub B. Ayoub)
3:27 Tatami :    • Visual Proof of AM-GM Inequality I   and    • AM-GM inequality visually  (attribution: Doris Schattschneider)
4:05 Semicircle :    • AM-GM Inequality II (visual proof)   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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