Mean Inequalities via Moments

Опубликовано: 26 Август 2026
на канале: Mathematical Visual Proofs

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This short animated proof demonstrates the two variable mean inequalities by use of moments of mass. #mathshorts #mathvideo #math #inequality #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #mathematics #physics #moments #weight #3b1bsome1 #some1

This animation of the Harmonic Mean/Geometric Mean/Arithmetic Mean/Quadratic Mean inequalities is based on a visual, physical proof by Tom Edgar that will appear in an upcoming issue of Mathematics Magazine. To read a preprint of the article (which contains alternate proofs of the same inequalities using centers of mass), see this link:

https://bit.ly/AMGM-Moment

Here is the published version from Mathematics Magazine (https://doi.org/10.1080/0025570X.2023... )

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)

To learn more about animating with manim, check out:
https://manim.community
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Intro/concluding music, used according to CC BY-SA 3.0, is "The Road" from Esteban Orlando:

Esteban Orlando:
  / orlando-esteba.  .
  / estebanorla.  .

https://creativecommons.org/licenses/...
Music provided by RFM:    • Video