The unexpectedly hard windmill question (2011 IMO, Q2)
3Blue1Brown 3Blue1Brown
0 subscribers
113K 1.5K

 Published On Aug 04, 2019

The famous (infamous?) "windmill" problem on the 2011 IMO
Help fund future projects:
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters:
Home page:

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:

You can find data for past IMO results here:

Viewer-created interactive about this problem:

And another:

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.


These animations are largely made using manim, a scrappy open-source python library:

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:

Stream the music on Spotify:

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:

Various social media stuffs:

show more