New video! Pi hiding in prime regularities
Added 2017-05-19 15:55:18 +0000 UTCHello all,
You might notice that this is the longest video I've ever made, coming in a 30 minutes. It's one of my favorite pieces of math, and exemplifies why I love number theory so much. The progression here is a nice example of a problem which walks the delicate line between achievable, and intractably complicated, and it feels like the universe is really giving you a hand by keeping things on the "achievable" side of that line.
Thanks to those who caught a few errors on the initial draft here.
-Grant.
Comments
One fun one is that you can arrive at the solution to Basel's problem by analyzing a lattice in 4-dimenions, which entails finding a way to count how many ways a number can be expressed as the sum of four squares.
3blue1brown
2017-05-31 15:30:43 +0000 UTCI really really loved this video. I am real curious what other formulas for Pi one could derive using different lattices (e.g. with equiliteral triangles) but didn't have time yet to ponder a little on that.
Lionel Pöffel
2017-05-30 19:58:32 +0000 UTCThanks for sharing! That is indeed surprisingly simple.
3blue1brown
2017-05-29 16:29:24 +0000 UTCI think the best proof of the fact at ~10:30 is found in this pdf: <a href="http://www.maths.lancs.ac.uk/jameson/foursquares.pdf" rel="nofollow noopener" target="_blank">http://www.maths.lancs.ac.uk/jameson/foursquares.pdf</a>
cinder_block
2017-05-26 23:48:32 +0000 UTCI'm a clinician data-scientist, and Grant, you're my only hope for a number theory enlightenment. Please continue making more videos like this one.
Tavpritesh Sethi
2017-05-26 02:44:44 +0000 UTCHey sorry for writing here, but I can't seem to write in the community without becoming a patron, which is my issue. I'm trying to become a patron and would like to pay with my PayPal balance, but this does not appear as an option, and so far I have not been able to resolve this on the PayPal side, so I'm just curious if anyone knows what's up here?
2017-05-23 08:35:01 +0000 UTCLove your long-form stuff! Keep it up!
2017-05-22 19:32:33 +0000 UTCGreat video! Thank you for that! (◕‿◕)
SexBook _____ ADULT PHOTO AND VIDEO SIGNATURES
2017-05-22 17:58:45 +0000 UTCGreat, came together perfectly at the end.
Manuel Garcia
2017-05-21 21:29:38 +0000 UTCThanks Alex, I really hope they do.
3blue1brown
2017-05-21 19:46:10 +0000 UTCAbsolutly! Or for quaternion in 4d, where you can stumbled upon the solution to the Basel problem. Somewhere on my list is to cover the proof of Fermat's last theorem for the case n=3 using The Eisenstein integers.
3blue1brown
2017-05-21 19:45:02 +0000 UTCPerfect.
2017-05-20 18:47:57 +0000 UTCOne of your best videos. Great work!
Alexey Badalov
2017-05-20 02:39:59 +0000 UTCLoved this video. Your work is amazing. These videos are going to inspire the smartest kids of future generations for years to come. (Also, nice Martin Sheen joke ;) )
2017-05-20 01:12:29 +0000 UTCGrant: for a fun extra excursion, try doing the same thing with a triangular grid (“Eisenstein integers”). :-)
Jacob Rus
2017-05-19 19:24:46 +0000 UTC
