A wonderful proof to Brouwer's fixed point theorem using the Hex game |
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- Опубліковано 27 чер 2024
- This video is in english because it is my SoME 2 project. I'll add french subtitles. I hope my accent isn't too awful.
First error spoted at 1:52 : g is defined over [0, 1] to IR ! (and not to [0, 1], I forgot to change the animation text ...)
link to David Gale's article : www.math.pitt.edu/~gartside/he...
animations made using Manim : www.manim.community/
All the python code of the video will be added to my github account, so check it out if you're interested.
Here is the link to my github : github.com/MatheFysyk
I hope you'll enjoy this video which took a little more than a month to make. If you have any suggestion or critic to help me and so that I can improve my work, don't hesitate to tell me.
00:00 Introduction
01:14 Fixed Points
03:20 Brouwer's Theorem
06:34 Hex Game
07:55 Hex Theorem
08:52 Hex Theorem Proof
11:30 Hex Theorem Recap and Gale's Article
12:30 Brouwer's Theorem Proof
14:08 Uniform Continuity Visualization
16:08 End Of The Proof
21:01 Conclusion And Credits
Very good video, great work :) ! Love the animations and the voiceover keep it going. Hope you'll be selected for the competition ;)
Thanks for your comment ! It's a lot of work, but I'm proud of the result, and even if I'm not selected for the competition, it was fun to make this video 🤗
La vidéo est vraiment clean et le sujet vraiment intéressant !! Merci et bravo
Nice video. I liked that you structured it as a story, not just focusing on the math. Good luck in the competition :-)
Thanks a lot for your comment ! Yes, I wanted also to talk a bit about the history and the background of this theorem, I think I'll keep doing this in the future :)
@@MatheFysyk I'm sure there's audience for this kind of content. Good luck finding it (hope UA-cam figures out quickly who those people are).
C'est incroyablement stylé
Impressionnant ! Bravo
Wow. C'est une vidéo magnifique!
You did a great job.
Before I saw this video, I had the idea of making a video about the Hex game and the Brouwer's theorem using manim :) and I was sure it will be very hard. So I understand how much you have worked for this. Thank you. I will probably use your codes for creating some more animations.
Btw I like your French accent too :)
Thanks for your comment ! (Sorry, I'm replying a bit late 😅) Feel free to use my code as you wish.
L'élite
La topologie c’est nul vaut mieux faire des flèches et dire que ça commute
Le meilleur, ça reste quand même de faire un dessin 😎