Visual irrationality proofs from the carpets theorem (root 2 and root 3)

In this video, we introduce and prove the "Carpets Theorem" and then utilize the theorem to prove that both the square root of two and the square root of three are irrational by a visual infinite descent argument.

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#irrationalnumbers #realnumbers​ #manim​ #math​ #mtbos​ ​ #animation​ #theorem​​ #visualproof​ #proof​ #iteachmath #mathematics #irrational #carpetstheorem #proofbycontradiction #root2 #algebra #infinitedescent

This animation is based on an argument from Stanley Tennebaum. If you are interested, I recommend this article from John Conway and Joseph Shipman about the irrationality of square root of two (and others):

To learn more about animating with manim, check out:
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Music in this video:

[QuantumHistorian]

You have to argue why (2b-a) and (a-b) are positive at every step of the iteration in order for the infinite descent to be a contradiction. It's not a particularly difficult thing to do, but without doing so the proof has a subtle hole in it as there is no contradiction in finding an infinite list of decreasing integers.

[josesilesramirez]

Beautiful! Very nice work and explanation! Thanks you for creating and sharing this content!

[jacemandt]

1:34 You said "suppose that √2 is irrational, " but I think you must mean "suppose that √2 is rational".

[primechords]

Hey! Your videos are really well done. I'm wondering what software you use to animate these and how long it takes for you to make one on average.

[KalaiarasiKalai-qzxk]

Bro in 0:46 why we add 'y' because the area is z. If its wrong please sorry

[davidaloha]

How would do you apply this type of visual proof to √5?

[AnglandAlamehnaSwedish]

Nice I like it ty for the link I used a similar one like this with chalk at the skateboard park writing it on the concrete as I did a kickflip noseslide revert I thought if we filmed tricks with math in chalk on the street n ledges then parents would buy the kids our company boards n I did the math n the tricks n our company would break off from traditional skateboarding crews n teams it's like urban or hesh or euro but maybe math would bring the skateboard world together with all the skaters in the world then of course life has other plans for you than the ones u make no matter how hard you try to keep on the right path, cancer, ppl drunk driving, deaths many many deaths n then skateboarding doesn't seem so important n the window is so small in your life to be pro maybe I could put together a team but I'm 44 now n full of injuries n no I didn't sue anyone except medical bills that I found out was covered by my insurance n I was too late on the statute of limitations dam I could of gave my daughter a good life or better than this shit she has now but he like mi Portuguese familia Tudo diga ES VIDA NOA E!!!