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

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

Рет қаралды 6,267

Күн бұрын

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
This animation of the inequalities is based on a visual proof by Roger Nelsen from the June 1987 issue of Mathematics Magazine (www.jstor.org/...) p. 158.
If you like visual proofs of inequalities, see these links:
AM-GM inequality via rectangles/squares: • Visual Proof of AM-GM ...
AM-GM inequality via circles: • AM-GM Inequality II (v...
AM-GM-HM-QM via Moments: • Mean Inequalities via ...
To learn more about animating with manim, check out:
manim.community

Пікірлер: 43

@gutzimmumdo4910 2 жыл бұрын

wow this is the best explanation ive seen great job!

@MathVisualProofs 2 жыл бұрын

Thank you! I love this proof but always have to think really hard about why each piece of the diagram is the way it is.

@bananaman4705 Жыл бұрын

These type of videos need more viewer :))

@MathVisualProofs Жыл бұрын

Glad you enjoyed this one! Share them with friends :)

@MathEnthusiast314 2 жыл бұрын

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

@MathVisualProofs 2 жыл бұрын

Thank you! Happy to be practicing and sharing visual proofs with others.

@wangryanlihci4597 Жыл бұрын

dude that's actually genius

@wangryanlihci4597 Жыл бұрын

respects given

@MathVisualProofs Жыл бұрын

It's a great visual proof right?

@wangryanlihci4597 Жыл бұрын

@@MathVisualProofs of course

@mach1553 2 жыл бұрын

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

@MathVisualProofs 2 жыл бұрын

Glad they are working for you! I’ve got more if you’re looking for others :)

@lovishnahar1807 10 ай бұрын

@@MathVisualProofs your teaching way is so reliable

@TheBasikShow 2 жыл бұрын

Very slick! I love it!

@MathVisualProofs 2 жыл бұрын

Thanks! Definitely a nice proof.

@alvarol.martinez5230 2 жыл бұрын

My favorite so far!!

@MathVisualProofs 2 жыл бұрын

Glad you liked it! Definitely a good way to do the mean inequalities. Thanks as always!

@subtlethingsinlife Жыл бұрын

Awesome ... Visually brilliant and elegant

@MathVisualProofs Жыл бұрын

Glad you liked it!

@Maths_3.1415 Жыл бұрын

This is beautiful :)

@MathVisualProofs Жыл бұрын

Thanks!

@LeeDeVilleMath 2 жыл бұрын

Very nice... short and sweet

@MathVisualProofs 2 жыл бұрын

Thanks! That’s the goal with my channel. Not many more than 4 minutes… longest is about 5. :)

@jakobr_ 2 жыл бұрын

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

@MathVisualProofs 2 жыл бұрын

Oh wow. That is a great idea. Beyond my skill set so far.

@NicolaiWeitkemper 2 жыл бұрын

@@MathVisualProofs Is your source code open? I'd give it a try.

@FromTheMountain 2 жыл бұрын

That sort of thing is actually quite easy to make in Desmos, here you go: www.desmos.com/calculator/dilnf6slzi. All you need to do is press the play button next to the definition of b. Unfortunately, as far as I'm aware, it is not possible to add text to the image in Desmos.

@MathVisualProofs 2 жыл бұрын

@@FromTheMountain thanks! I definitely know this can be done in Desmos and GeoGebra pretty easily. If I had thought about your suggestion before the programming, could have done it differently to make it easier to implement in manim (should be easy but not how I did it). Thanks!

@spikypichu 2 жыл бұрын

so cool! I have to share :)

@MathVisualProofs 2 жыл бұрын

Appreciate it!

@thalestassi 2 жыл бұрын

Amazing video, you provide the code of your videos?

@MathVisualProofs 2 жыл бұрын

I haven't yet, but people have requested. The code is messy, but people claim they don't care. I will work on creating a repo at some point I hope.

@teachmath3394 4 ай бұрын

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

@sidimohamedbenelmalih7133 11 ай бұрын

How to show visually that HM+RMS

@MathVisualProofs 11 ай бұрын

Good question! I’ll see if there’s a nice one.

@math2693 2 жыл бұрын

Waaaaaw!!!!! This is a waw channel

@bananaman4705 Жыл бұрын

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

@MathVisualProofs Жыл бұрын

The idea is at each stage one of them is the leg of a right triangle and the other is a hypotenuse. So the hypotenuse is always longer than the legs.

@rounakgongle 10 ай бұрын

what is QM?

@MathVisualProofs 10 ай бұрын

Quadratic mean. Also called root mean square

@rounakgongle 10 ай бұрын

@@MathVisualProofs I am in love with your content ❤️ as I am already interested in geometry....Can you recommend any geometry book for theory as well as problem solving?