Sneaky Topology
Added 2018-11-18 14:12:21 +0000 UTCHey Everyone,
Iβve been traveling a fair bit this month, so have had less time for usual video production. To help fill the gap, I went back to do a refurbishing of an old video. For one thing, it had a number of errors I wanted to correct, to include some typos, very poor sound quality, etc. I also wanted to replace the proofy bit in the middle with a better argument, since the argument from the previous video was actually slightly incorrect, and now it ties nicely to the idea of winding numbers.
Needless to say, no charge on this one. The bulk of it it was already patron supported back in the day (and the end credits reflect the patrons at that time). This is simply breathing a bit more life into a lovely topic which Iβd like to exist in its best form in perpetuity.
Genuinely new content to come soon!
-Grant
Comments
Nice
2019-01-31 16:48:21 +0000 UTCNice ... wish i could pledge to 3b1b, Kurzgesagt, Inkstall and Lemmino.. One day i will :)
Roshan Shetty
2019-01-24 08:30:35 +0000 UTCGood ;-)
2019-01-17 19:12:18 +0000 UTCThis is really nice. It's hard for me to see, though, how you would generalize the proof of the Borsuk-Ulam Theorem to higher dimensions, since the proof you gave seemed to rely on taking a path (which is one-dimensional) from a point to its antipode and then retracting that path down to a point. Is the proof of the theorem completely different in higher dimensions, or do I just need to learn a bit more higher-dimensional homotopy theory to understand how you can generalize the proof you give in this video? I'm also curious about which part was incorrect in the previous version. Thanks again for your great work!
Daniel and Rebekah Slonim
2019-01-01 17:31:34 +0000 UTCNicely done!
Programmable Spacecraft
2018-12-18 21:45:30 +0000 UTCPlease become my patron
Science Is Art 101
2018-12-17 12:28:27 +0000 UTCThe beauty of Math <3
2018-12-02 03:25:35 +0000 UTCFine :-)
2018-11-27 10:09:52 +0000 UTCDidn't know Markus Persson (Notch) supported the work.
2018-11-19 07:27:48 +0000 UTCMy father was a topologist (among other things he worked on the visualization of the eversion of the sphere) and I really appreciate your ability to explain some of the concepts and applications of topology in your videos- it brings me just a little closer to him (he passed away when I was but 10...).
Gregor Shapiro
2018-11-19 06:57:03 +0000 UTCThanks! As I said, I really like this piece of math, and I feel happier now with how it exists on the channel.
3blue1brown
2018-11-19 00:12:52 +0000 UTCAs usual, elegantly engaging.
2018-11-18 17:14:05 +0000 UTCFantastic. That was REALLY well constructed.
Don Sanderson
2018-11-18 16:14:50 +0000 UTCThis is probably my favourite of all of your videos, and I'm so glad it got a touch up. The new proof is really cool, definitely gonna use it next time I'm boring my friends with amazing math facts.
Isobel Taylor
2018-11-18 15:51:36 +0000 UTC
