Mean Inequalities via Moments #SoME1 #3b1b (visual proof)
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:
If you like visual proofs of inequalities, see these links:
AM-GM inequality via rectangles/squares:
AM-GM inequality via circles:
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Intro/concluding music, used according to CC BY-SA 3.0, is “The Road“ from Esteban Orlando:
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