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.
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
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.
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.
You might like this : th-cam.com/video/HFGSsPbYc-s/w-d-xo.html (older video so my animating skills weren’t as good)
Wow! I love this!
👍😄
Love these visual proofs man :)
Thanks
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
Very Great...👌👌👍👍👍👍
Thanks!
Great!
Nth root of any number how to visualize that..
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.
Geometric mean to rms inequality
Take this diagram and merge it with the one here : th-cam.com/video/jNx05gXSblE/w-d-xo.html :)
@@MathVisualProofs What about Rms to Metallic mean inequality
Is that AM GM inequality ?
No. This is though : th-cam.com/video/jNx05gXSblE/w-d-xo.html