Arithmetic Mean-Geometric Mean Visual Proof Compilation

This video is a compilation of seven shorter videos that I have created showing various visual proofs without words of the famous AM-GM inequality, which states that the arithmetic mean of two numbers (a+b)/2 is greater than or equal to the geometric mean of the two numbers square root of a times b.
To see the original videos (in shorter form and sometimes with words/explanations), check the links below. Of course there are many other visual proofs of this amazing fact, but these are my favorite seven.
Let me know your favorite in the comments!
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualPr.... Thanks!
Here are the original series videos (along with attribution; for more detailed attribution, see the original videos):
0:00 Introduction
0:05 Folding Proof : • Folding the AM-GM Ineq... and • Fold the AM-GM inequality (attribution: Yukio Kobayashi)
0:40 Circle with Triangles : • Mean Inequalities (vis... (attribution: Roger B. Nelsen)
1:07 Sliding Triangles: • AM-GM Inequality III (... (attribution: Claudi Alsina and Roger B. Nelsen)
1:52 Tangent Circles : • AM-GM Inequality IV (v... (attribution : Roland H. Eddy)
2:38 Eight Kites : • AM-GM Inequality VI (v... (attribution: Ayoub B. Ayoub)
3:27 Tatami : • Visual Proof of AM-GM ... and • AM-GM inequality visually (attribution: Doris Schattschneider)
4:05 Semicircle : • AM-GM Inequality II (v... and • AM-GM Inequality II (attribution: Charles D. Gallant)
4:49 Ending citation
If you like this inequality or others, you can check out my playlists of inequalities and AM-GM inequality:
Inequalities: • Inequalities
AM-GM : • AMGM Inequality
#math #amgminequality #area #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo #inequality #inequalities
To learn more about animating with manim, check out:
manim.community

[@kextrz]

Wow! This might just be the most impressive and useful math video I've ever seen. Bravo!

[@MathVisualProofs]

Glad it was helpful!

[@mauisstepsis5524]

Amazing video, cool music is a bonus too!

[@MathVisualProofs]

😎🎵

[@Dhanika112]

I love this concept, it is going on now in my maths coaching

[@MathVisualProofs]

👍😀

[@STEMHub18]

IIT coaching?

[@Nothingx303]

Why this is so satisfying and interesting 😊😢

[@MathVisualProofs]

😀

[@GovindShukla-cc6ul]

you are awesome

[@MathVisualProofs]

Thanks!

[@GovindShukla-cc6ul]

@@MathVisualProofs btw what's your age sir?

[@carlosrocha3833]

Fantastic

[@MathVisualProofs]

Thanks!

[@moscripts]

This is beautifu! and delightful to watch! Pls what software/tool do you use for your animations?

[@MathVisualProofs]

I use manim for these (python library from 3blue1brown)

[@Dhanika112]

Can you make a video on this concept on why x +1/x range. Is( -infinite,-2] and [2, infinit)

[@MathVisualProofs]

These essentially prove that. I have four shorts investigating that variation of these.

[@Dhanika112]

@@MathVisualProofs 😊okay , I am going to watch those

[@melchorkinghilarioesquillo8899]

Elegant ❣️

[@MathVisualProofs]

😎👍

[@turtlgamez]

I don’t understand some of it but it looks like it makes sense

[@appybane8481]

Many of them are cool. However, some of them are just proving that (a+b)^2=(a-b)^2+4ab then simplify.

[@MathVisualProofs]

Yes. That is essentially the proof of am-gm so you expect visual proofs to reflect that but geometrically.

[@xjuhox]

How about using the geometrical multiplying as a basis of proof? That is, if we have a,b > 0, we can construct the product a*b.

[@realshavez]

Bro please Give Your video Source code 😢😢

[@natashok4346]

Hey, diddle diddle, the median is middle...
😜