Arithmetic Mean-Root Mean Square Inequality (visual proof)

[@curtiswfranks]

Not an obvious proof method to me (although I suspect that all generalized means might be expressible in a nice graphical way), but totally intuitive once I have seen it. This is how I will remember this. Elegance itself.

[@MathVisualProofs]

You might like this : th-cam.com/video/HFGSsPbYc-s/w-d-xo.html (older video so my animating skills weren’t as good)

[@張惟淳-d2f]

Wow! I love this!

[@MathVisualProofs]

👍😄

[@MathOrient]

Love these visual proofs man :)

[@MathVisualProofs]

Thanks

[@Ninja20704]

My teacher taught us to prove this inequality using the cauchy schrawz inequality, as that method can be used to generalise the result when we have n terms instead of only 2. Still good video

[@easymath599]

Very Great...👌👌👍👍👍👍

[@MathVisualProofs]

Thanks!

[@ronflypotato4242]

Great!

[@darogajee3286]

Nth root of any number how to visualize that..

[@pkskyutube]

This is really beautiful, but when I tried applying this geometry to prove or demonstrate simple arithmetic means, I got completely lost. And also, I'd like to see how this extends to more than one sample, a, b, c, ... Amazingly I searched TH-cam and found no geometric proof of the Arithmetic Mean anywhere, only proofs of the various mean inequalities and no proofs extended to more that one sample.

[@jhgvvetyjj6589]

Geometric mean to rms inequality

[@MathVisualProofs]

Take this diagram and merge it with the one here : th-cam.com/video/jNx05gXSblE/w-d-xo.html :)

[@jhgvvetyjj6589]

@@MathVisualProofs What about Rms to Metallic mean inequality

[@kaaristotelancien3005]

Is that AM GM inequality ?

[@MathVisualProofs]

No. This is though : th-cam.com/video/jNx05gXSblE/w-d-xo.html