There's more to 3B1B's absurd circle division pattern video | Hyperplane Arrangements

Original Title of this video: "3B1B There's a problem with your absurd circle division pattern video"

There's a tiny detail in the statement of Moser's Circle Problem that Grant gives that is a bit off if you think about it too much, and if you decide to address it like I do in this video we run into a different circle division problem, the lazy caterer problem, which gives rise to the lazy caterer's sequence and yet another connection to Pascal's Triangle. Continuing we also wander into the field of Hyperplane Arrangements. If you like thinking about the combinatorial nature of Moser's Circle problem presented in the 3Blue1Brown's video, you may be pleasantly surprised that problems like it are not just some piece of popular mathematics, but a whole mathematical industry in the research world in their own right. Hopefully this video finds you well!

Books on Hyperplane Arrangements:

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WHAT GEAR I USED FOR THIS VIDEO:

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#CHALK #3B1B #Hyperplanes

[XoroLaventer]

Good video, but I think it would've been better without constructing the title and the thumbnail in such a way that you have to explain you didn't mean it that way for the first 3 minutes of the video

[michaeldamolsen]

What I really liked in Grant's video was that it only used terms and concepts that I was already intimately familiar with, to explain something that wasn't obvious to me from the start.
What I really liked in your video was that it introduced me to a lot of new tools and concepts, to explain something I was already intimately familiar with.
I love the duality between these two videos, thank you for posting this.

[aylerayler]

Very cool way of splitting up the vector space layers with the editing, I mean. 👌

[brycenbg]

in 3:39/23:14, I think the problem is that 3B1B does THE NUMBER OF POINTS ON THE CILCLE first then connects it to the other points to produce the maximum divided region but what you do is you use THE NUMBER OF LINES to directly cut the circle to produce the maximum region. Therefore I think that you and 3B1B are doing a completely different question.

[compegord]

You’re a gem. It’s been a privilege to see you grow.

[explosionspin]

having read about matroids I kept hearing about hyperplane arrangements. Math feels so huge like... I'll never have enough time to understand all these areas of math and how they connect together.

[OllieClarke]

Thanks for the video! There's a very nice web of mathematics here. One path through this web that I like is from Hyperplane Arrangements to Matroid Theory to Tropical Geometry - all of which are big fields in their own right but also connect together.

[kurtiswright]

Awesome video, off to go read more about Hyperplane Arrangements!

[KingGumbly]

This kind of nitpicking is great because its like "yes, but no, but what if?" Great video keep it up! :D

[jm-xhyz]

I have been hobby studying function physic based math. Then you come in with this 'but maybe just a little bit weirder now' math core math and... I don't know you, Nathan, but you have made my astrophysics hobby complicated

[muskyoxes]

"A video about intuition didn't formally articulate every premise!"

[rarebeeph]

that structure you drew at 18:47 reminds me very strongly of diagrams i've seen representing abstract polytopes

[abdjahdoiahdoai]

what’s wrong with thinking complex number as a plane?

[geopicaltrometry]

If you found this interesting, I also suggest watching June Huh's 2022 ICM talk as it involves generalizations stemming from the considerations made here (also it is just a great talk overall).

Great video Nathan!

[willnewman]

Good video, though I feel the title and thumbnail are a bit too much

[AK-vxdy]

Your addiction to chalk is marvelous ;)

[jonathanberry]

Are the lines intersecting, or converging? Consider that if these lines were paths there would be no "intersection" of the paths, there is no crossing of paths.

[ameliaC-xgrg]

Cool video! Could I make a suggestion for future videos: Personally I would really love to see some videos about cool theorems in analysis(in particular, measure theory) and how they get applied in real-world math research. Also advice about applying to math grad school would be really helpful :P I really appreciate your content, please keep it up!

[zafarb]

Reported for Misleading Content👍. Great Job on the title

[insouciantFox]

The fact that I can't see your chalk when you're writing gives me anxiety.