This problem seems hard, then it doesn't, but it really is

The famous (infamous?) Problem 2 on the 2011 IMO
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You can find data for past IMO results here:


The full list of problems considered for the IMO that year, together with their solutions, can be found here:


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.


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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.
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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.

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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:

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