AM-GM Visual Proof VII @MathVisualProofs

Uploaded June 2026 | Updated September 2026, 2 weeks ago

AM-GM Visual Proof VII

This is a short, animated visual proof demonstrating the arithmetic mean geometric mean inequality using areas of squares with square root side lengths and rearranging areas.

This animation is based on a visual proof from Alfinio Flores that appeared in the March 2000 issue of The College Mathematics Journal (vol 31, no 2 p106) jstor.org/stable/2687579

f you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!

For other visual proofs of this fact see:

youtu.be/Pt8IX_Q5U1A
youtu.be/62G9fak1vyk
youtu.be/HFGSsPbYc-s
youtu.be/SEPkdPWKdO0
youtu.be/jNx05gXSblE
youtu.be/IJGwvvQdfgg

#math #amgminequality #manim#proofwithoutwords #visualproof

To learn more about animating with manim, check out:
https://manim.community

$Chaos in a Heptagon! In this short, we show what happens when iterating the procedure of choosing a heptagon vertex at random and moving 0.692 of the distance from the current dot to the chosen point. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you want to know more about the Chaos game, see the following links: https://en.wikipedia.org/wiki/Chaos_game https://mathworld.wolfram.com/ChaosGa... https://math.bu.edu/DYSYS/chaos-game/... https://youtu.be/kbKtFN71Lfs https://youtu.be/IGlGvSXkRGI https://youtube.com/shorts/yDHkNDrHfIw #chaos #chaosgame #heptagon #mathvideo #math #mtbos #manim #animation #theorem #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractal #fractals To learn more about animating with manim, check out: https://manim.community$

$Mediant Inequality from Slopes This is a short, animated visual proof demonstrating what one might call the mediant inequality. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! For an alternate visual proof of this fact, see: https://youtu.be/RKeBuWL1B4A https://youtube.com/shorts/cI92ZID95g4 https://youtu.be/pODylgdI3p8 For the wide format of this video, see: https://youtu.be/AuxqpiDTCyU?si=kLa0Un4L8ADM6a_q This animation is based on a visual proof by Li Changming from the January 1988 issue of Mathematics Teacher (https://www.jstor.org/stable/27965677 - page 63). #math #inequality #numbertheory #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #fractions #mediant #mathematics #fareyfractions #farey #mathshorts #mathvideo To learn more about animating with manim, check out: https://manim.community$

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