AM-QM Inequality (2-D; visual proof) @MathVisualProofs

Uploaded December 2025 | Updated September 2026, 2 weeks ago

This is a short, animated visual proof demonstrating the arithmetic mean quadratic mean (or root mean square) inequality for two and variables using rectangles.

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The visual proof in this video is based on a proof without words by David Treeby from the June 2022 issue of Mathematics Magazine ( tandfonline.com/doi/full/10.1080/0025570X.2022.2054650 page 241).

For other visual proofs of inequalities check out this playlist:
youtube.com/playlist?list=PLZh9gzIvXQUuKcFHdtjFkwAVELDxu9nH4&si=f4AHNOU1iTWO8Xb_

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

Function Proof via Diagram Chasing (g composed f injective and f surjective implies g injective).

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$Wallis Sieve Area! In this short, we show how to build the Wallis Sieve using an iterative procedure of cutting remaining square lengths into the next odd and removing the created central square in the corresponding square grid. Along the way, we discuss how to compute the area of the resulting limiting shape as an infinite product. This infinite product is related to the famous Wallis product and so the shaded area is amazingly Pi/4. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you want to know more about the Wallis Sieve, check out this wonderful short article by Evelyn Lamb: https://www.scientificamerican.com/blog/roots-of-unity/a-few-of-my-favorite-spaces-the-wallis-sieve/ #mathvideo #math #mtbos #manim #animation #iteachmath #mathematics #dynamicalsystems #fractal #fractals #wallissieve #wallis #wallisproduct #infiniteproduct To learn more about animating with manim, check out: https://manim.community$

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