Visual irrationality proofs from the carpets theorem (root 2 and root 3)
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- Опубликовано: 9 сен 2024
- 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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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):
dev.mccme.ru/~m...
To learn more about animating with manim, check out:
manim.community
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Music in this video:
Air Hockey Saloon by Chris Zabriskie is licensed under a Creative Commons Attribution 4.0 license. creativecommon...
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Artist: chriszabriskie....
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.
I did say they are positive and the geometric argument here should show it. Agree that to do it formally you want to prove the inequalities work.
Since they are geometric lengths, they are automatically positive. That is an advantage of the geometric proof over the an algebraic one.
integer - integer = integer
Beautiful! Very nice work and explanation! Thanks you for creating and sharing this content!
Thanks for checking it out!
1:34 You said "suppose that √2 is irrational," but I think you must mean "suppose that √2 is rational".
Whoops! Thanks for catching it. I definitely meant suppose that root 2 is a rational but my brain must have slipped to irrational
I think I was able to clip the slip up and it shouldn't cause a problem. I appreciate you catching it!
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.
Thanks for the comment! I am still learning. I use ManimGL to do the animations. At some point I need to move over to the community edition of the software. How long depends on what I’m doing and how efficiently I go about doing it. Most of the short videos don’t take much more than 2-4 hours of dedicated coding time. This one here took longer because I did one version where I couldn’t automate the infinite descent repeating so I redid it. I’ve been playing with this idea for a few months so I can’t pinpoint how much time I spent on this one.
Bro in 0:46 why we add 'y' because the area is z. If its wrong please sorry
How would do you apply this type of visual proof to √5?
Try it in a regular pentagon... there is an article linked in the description that has a picture that might be helpful in figure 2...?
Is that the .ru link?
@@david0alohayes.
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!!!
무한강하법...
Yes! I love that this visualizes infinite descent trough I didn’t want to show it descend forever :)
@@MathVisualProofs you are always amazing. You should know that
@@user-lr8od4uz1n appreciate this! Thanks :)