Mean Inequalities (visual proof of AM-GM, HM-GM, and AM-QM inequalities)

This short animated proof demonstrates the two variable mean inequalities for the arithmetic mean, geometric mean, harmonic mean and root mean square (or quadratic mean). #math​ ​#manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #inequality #iteachmath #mathematics #pythagoreantheorem #similartriangles #means #meaninequality #mathshorts​ #mathvideo​ #mtbos

If you like visual proofs of inequalities, see these links:

To learn more about animating with manim, check out:

[gutzimmumdo]

wow this is the best explanation ive seen great job!

[MathEnthusiast]

This is such a beautiful video! Just discovered your channel and it's amazing!

[mach]

Watching videos like this I've learned more in weeks than I did in years. 👍🏼👍🏼

[subtlethingsinlife]

Awesome ... Visually brilliant and elegant

[bananaman]

These type of videos need more viewer :))

[thalestassi]

Amazing video, you provide the code of your videos?

[teachmath]

Hello my friend
Can you ecompose a number into the sum of two squares
Thank you very much

[jakobr_]

It would be really cool to see an animation of this diagram with b ranging from 0 to a

[bananaman]

How did you know those 4 must be less than or equal to in order from least to great from triangle proof?

[sidimohamedbenelmalih]

How to show visually that HM+RMS<AM+GM?

[eliotvarda]

I just don't see how that yellow segment is (a+b)/2? Everything else is fine, but i don't see that conclusion, ...