Mean Inequalities via Moments #SoME1 (visual proof)

This short animated proof demonstrates the two variable mean inequalities by use of moments of mass. #mathshorts​ #mathvideo​ #math​ #inequality #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #mathematics #physics #moments #weight #3b1bsome1 #some1

This animation of the Harmonic Mean/Geometric Mean/Arithmetic Mean/Quadratic Mean inequalities is based on a visual, physical proof by Tom Edgar that will appear in an upcoming issue of Mathematics Magazine. To read a preprint of the article (which contains alternate proofs of the same inequalities using centers of mass), see this link:

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

To learn more about animating with manim, check out:
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Intro/concluding music, used according to CC BY-SA 3.0, is "The Road" from Esteban Orlando:

Esteban Orlando:

[linguamathematica]

The lever and weights proof method is ingenious and provides a fantastic visualization of the underlying equations

[aashsyed]

great work! keep the super awesome work up! every second is valuable!!!! awesome!!!!

[aashsyed]

this is a nice lesson! and i appreciate even more cause it's a little bit of physics!! double enjoyed :)

[donaldhobson]

Each of these can be seen as f^-1(mean(f(x))) where f is 1/x, log(x), x, x^2 resp.

The harmonic mean (H=harmonic, M=mean) of a, b, c, d ie H(a, b, c, d)= H(H(a, b), H(c, d))<= M(H(a, b), H(c, d))<=M(M(a, b), M(c, d)) Generalizing, the means stay in that order whenever the number of inputs is a power of 2, and taking limits with repeats, the ordering always holds.

[shubhamg]

Guess I'm binging all your videos now hahaha.

[missingtourist]

Now that’s what I call a well-balanced equation! 🤣

[alvarol.martinez]

Very cool, your channel should blow up soon

[pardeepgarg]

*"Give me a world to stand and with a lever*
*I will move the whole world"*

[neoteric]

hey how much time it is taking for writing code for this much length of video's

[Josealves-qtwf]

I didn’t undestand why the distances are multiplied by the masses?