Solving the Challenging 2011 IMO Windmill Problem 🧠

The famous (infamous?) "windmill" problem on the 2011 IMO Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/windmillthanks Home page: https://www.3blue1brown.com The author of this problem was Geoff Smith. You can find the full list of problems considered for the IMO that year, together with their solutions, here: https://www.imo-official.org/problems/IMO2011SL.pdf You can find data for past IMO results here: https://www.imo-official.org/ Viewer-created interactive about this problem: https://www.reddit.com/r/3Blue1Brown/comments/d0b0qw/interactive_windmill_visual_program_download_link/ And another: https://aalluri7.github.io/windmill/ I made a quick reference to "proper time" as an example of an invariant. Take a look at this minutephysics video if you want to learn more. https://youtu.be/WFAEHKAR5hU Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown