x plus 1/x is greater than or equal to 2 when x is positive II (visual proof)

This is a short, animated visual proof demonstrating that sum of a positive real number and its reciprocal is always greater than or equal to 2. #math​ #manim​ #visualproof​ #mathvideo​ #geometry #mathshorts​ #algebra #mtbos​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #proof​ #iteachmath #inequality #pythagoreantheorem #amgm

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It turns out that this theorem is equivalent to the Arithmetic Mean-Geometric Mean inequality. The equivalence is implied by the following two proofs:    • Visual Proof of AM-GM Inequality I  
   • x + 1/x is greater than or equal to 2...  

This animation is based on a proof by Roger B. Nelsen from the December 1994 issue of Mathematics Magazine, page 374 (https://doi.org/10.2307/2690999). You can find this here too: https://www.maa.org/sites/default/fil...

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

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Music in this video
Megaepic by Alexander Nakarada | https://www.serpentsoundstudios.com
Music promoted by https://www.free-stock-music.com
Attribution 4.0 International (CC BY 4.0)
https://creativecommons.org/licenses/...