The windmill video is live (now with a real ending!)

That could be fun indeed! This is only tangentially related, but it also reminds me of "Buffon's needle", which seems like it could benefit from a clearer explanation of why exactly pi shows up.

3blue1brown

A great video. This so-called theme of "dots and sticks on a plane" is really common in probability problems, and more specifically in problems regarding the probabilistic method, where usually a universal solution is to be achieved (unlike an existensial one, as shown in your video). Perhaps if one day you would return to work on your probability series, you could reuse those animations... ;)

Thanks for such an encouraging comment. I'll try to keep it up!

3blue1brown

I love this. I love this SO MUCH. This is exactly the kind of insight that should be provided in a book, please 3b1b, make a collection of problems with a scientific moral, it will save the world! Gather knowledge from maths, physics and chemistry and coagulate it in a consumable form. You're the chosen one, embrace your destiny!! :P I am a chemist and I'm telling you, it has to be done by a mathematician passioned about teaching for our useless minds are nor developed enough to get maths properly. It's what every kid/smart highschool student/uni student is waiting for from the dawn of time, and it would change the world in a better place.

I *love* it.

Dragi Raos

I just chose a random pixel from the flag and used that color.

3blue1brown

At around 0:06, is there a significance to the colors used for the six dots representing the participants from each country?

Thanks!

3blue1brown

Indeed, that graph is broken into cycles (since the process is reversible). But it's very hard to progress to a solution from there, since you need to encode the geometric information about your points somewhere in that graph, which otherwise ignores all that structure.

3blue1brown

Thanks for the kind words. I think the reality is that even most people with graduate degrees would not do that well on the Putnam. On the one hand, part of what you learn are problem solving abilities, but realistically graduate degrees are more about gaining domain knowledge and original research experience in one specific subtopic. The kind of problem-solving the Putnam tests for is related, but perhaps largely orthogonal. At least that's my guess.

3blue1brown

I really love what you are doing with these--and all of your--videos: not just giving an answer but talking about how you might gain insight into them so you could solve them. Back to the Putnam test, now that you are no longer an undergraduate, you have a (or several?) graduate degree(s) and you are teaching mathematics, if say 100 people with similar credentials as you sat down to take the Putnam test with the same constraints as during the testing, what do you think the median score would be? A lot more than 1 or 2 I would hope. How much do you learn about generally solving problems during a mathematics degree? Would the median be 30? 60? More? Or is problem solving not really taught that well in college?

Given a set of points, we can form a "configuration graph" where the vertices are pairs (pivot point, sector the line is in), and every vertex has one outgoing edge to the next configuration. I wonder whether the structure of this graph can be described concisely. The video has shown that there's a cycle corresponding to vertices on the convex hull, and that there are cycles which visit every pivot point.

That was a very nice ending! I can certainly relate to not being able to understand how not everyone has an intuitive understanding of "simple" math. I remember a couple of years ago when taking a diving course, and the instructor was struggling to remember how to compute remaining air supply time at a given depth (pressure) while I was deriving it on the fly through intuition and dimensional analysis. It truly is hard to understand how that can not come as naturally as catching a ball.

You nailed the finish!

Great video, great morals. I was thinking about this in terms of the concept of reversibility from physics, since it has the same properties if it's played backwards. If there's a state (ie circling the convex hull) that it can't come back from, it wouldn't be able to get there in the first place, but your solution was much more elegant.

Robin Turtleson

Superb ending. Kind of a solution to a hard problem in itself (that seems obvious only in retrospect)

Daniel Raynaud

This is phenomenal. Easily one of your best videos.

Love this ending, really well done. Nice job.

Mark Mulvey

I like the end very much especially the comparison to tales. Thanks for the great video!

Awesome video!!!

Aniket raj

I loved the final touch of Don Quijote y Sancho.

Daniel Armesto

I really like where you took this, Grant.

Stacey Greenstein