New video! Who (else) cares about topology
Added 2017-02-10 20:01:03 +0000 UTCDearest patrons,
This is a beutiful piece of math, a platium-level proof if ever there was one. I'm a bit of a sucker for anything that connects two disparate ideas in math (who isn't?), so when I first came accross this it immediately jumped towards the top of my video list.
Much like the first "Who cares about topology" video, a strong motivation in making this is to show how ideas from this field can actually be used to solve problems. Sure, any time you squish a sphere onto a plane some antipodal pair must land on each other, but who cares? And as with the first video, the upshot comes down to constructing a clever function an showing that there must be some collision.
Also, it was fun to have a bit of coordination and cross-promotion with Mathologer. Hopefully at some point in the future we'll do a proper collaboration, though it's hard given that we're almost at antipodal points of earth ourselves.
I hope you enjoy,
-Grant
Comments
I have a fun math problem for you guys to solve if you are interested. If you have a solution I'd love to hear your reasoning: <a href="https://docs.google.com/document/d/1-GUlwT0SQyr_tvRzrkcg0IExXSPIxpNCnl9xgwWOXpo/pub" rel="nofollow noopener" target="_blank">https://docs.google.com/document/d/1-GUlwT0SQyr_tvRzrkcg0IExXSPIxpNCnl9xgwWOXpo/pub</a>
Benjamin BairMoshe
2017-02-13 22:56:12 +0000 UTCYour videos do not disappoint. This right here is what is beautiful about math and science, finding the connection between two unrelated things, and seeing how they are actually two different ways of looking at the same problem. In Physics the problem is understanding reality, but in math it's whatever rules that create the problem.
Benjamin BairMoshe
2017-02-12 09:48:01 +0000 UTCGreat job, Grant. Fascinating video. The proofreader in me couldn't help but notice "minize" instead of "minimize" in one spot, and "theif" instead of "thief" in a few places. Probably too late to fix that, but it certainly didn't impact the impactfulness of the video.
Steve Muench
2017-02-12 04:18:08 +0000 UTCHaha, that's a true level of engagement right there. It's interesting to think about what the "expected" number of cuts one might need are, and how that changes for more jewels, because here I was just shuffling randomly.
3blue1brown
2017-02-11 18:15:44 +0000 UTCWhat a fantastic video about a fantastic proof! I've never really seen the "continuization" of discrete problems before– something I'll certainly have to try out.
Joseph Cutler
2017-02-11 12:17:05 +0000 UTCI love that you share such inspired proofs with fantastic visualizations/explanations. Though I'll admit that I got distracted noticing that most of the stolen necklace problem images could be solved with one fewer cut. =P
Evan Miyazono
2017-02-11 00:06:16 +0000 UTCThanks to kind folk like you, Albert, I won't :)
3blue1brown
2017-02-10 22:34:37 +0000 UTCamazing video! please dont stop
Albert Martinez
2017-02-10 22:14:03 +0000 UTCYup! He posted at the same time. It's a wonderful little argument using Sperner's lemma that he describes. Sperner's lemma is one of those things worth learning about just because it comes up in so many unexpected contexts (like proving the Brower fixed point theorem).
3blue1brown
2017-02-10 21:31:55 +0000 UTCThank Troy. There's also a typo earlier where I write "Minize" instead of "Minimize". I am much too prone to these slips.
3blue1brown
2017-02-10 21:30:46 +0000 UTCThat was great. I take it the Mathologer video is forthcoming.
john kraemer
2017-02-10 21:11:31 +0000 UTC
