Arithmetic mean vs Geometric mean | inequality among means | visual proof

hi~

It's quite hard to upload videos from china because of YouTube being banned, but I'll be back home in two/three months and will be uploading more frequently (i will try at least).

Same thing with Patreon..

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Support my animations on:

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Any further questions or ideas:

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Programs used:

- Cinema 4D

- Adobe Premiere Pro

- Processing
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Music:

"so far away" by outlax

[Mathologer]

Very nice as usual. Your videos really deserve to be known more widely :)

[iorek]

This is one of the most under-viewed, under-rated videos I've found to date. Well done.

[diligar]

This is such a beautiful way to show that inequality! I’m absolutely blown away

[aldolunabueno]

I love your content, and I feel identified with it. Some time ago I discovered "Proofs without words", and was completely fascinated. See a figure for five minutes, and then, like a lightning bolt, realize how obvious it was. Most people will never use the mathematics that goes the most to add and multiply. If this were taught in schools, at least then they could tell how beautiful it is. I hope you keep growing, and that you have the support you deserve for this job.

[AlexandrBorschchev]

this is the most creative and unique math channel ever hands down. just out of the world talent, you can't find any other channel that does this.

[atomiccompiler]

I love your videos, they are really the bestest best over the whole youtube, and nothing gives me goosebumps like when I see your notifications. Please don't ever stop ! ♥

[KnThSelfThSelfBTrue]

Here from 3b1b! Really solid visual explanations. Very intuitive.

[ashutoshmahapatra]

Your videos are my definition of perfect.

[satyambhatia]

You're doing a great job. Keep it up. Your channel surely deserve more followers.

[plominecraft]

Awesome video man!

Keep the hard work :D

[ThoughtsEtcEtcEtc]

Such a great video and visualization. ❤️🙏

[vpambspt]

Nice to know you're "back" ^.^

[michalnemecek]

Nice visualization of the geometric mean. BTW how do you visualize the geometric mean of 3 numbers?

[txikitofandango]

Great animation! It's very clear that h must always be less than or equal to r, but how would you prove that rigorously?

[FatihKarakurt]

Visuals are great, I think music may need more attention!

[aleksandersabak]

How about the unloved harmonic mean? 2/(1/a + 1/b)? I kow it's allways smaller or equal to the geometric mean, but is there a nice graphical proof like this?

[Magnasium]

This is a great visualization! I'm not sure if your style is to teach or guide, but I felt the ratios at similar triangles thing went too fast

[brogcooper]

What is this genre of music called and what else is similar? It's not something I would normally listen to but I really like it.

[NoNTrvaL]

That was awesome! The music is too. What is its name?

[bhavyajainnd]

What an amazing analogy. I know an arithmatic proof but this is way prettier