Mean Inequalities (visual proof of AM-GM, HM-GM, and AM-QM inequalities)

This short animated proof demonstrates the two variable mean inequalities for the arithmetic mean, geometric mean, harmonic mean and root mean square (or quadratic mean). #math​ ​#manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #inequality #iteachmath #mathematics #pythagoreantheorem #similartriangles #means #meaninequality #mathshorts​ #mathvideo​ #mtbos

This animation of the inequalities is based on a visual proof by Roger Nelsen from the June 1987 issue of Mathematics Magazine (https://www.jstor.org/stable/2689561) p. 158.

If you like visual proofs of inequalities, see these links:

AM-GM inequality via rectangles/squares:    • Visual Proof of AM-GM Inequality I  

AM-GM inequality via circles:    • AM-GM Inequality II (visual proof)  

AM-GM-HM-QM via Moments:    • Mean Inequalities via Moments #SoME1 ...  

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