3Blue1Brown | Researchers thought this was a bug (Borwein integrals) @3blue1brown | Uploaded 1 year ago | Updated 2 hours ago
A pattern of integrals that all equal pi...until they don't.
Next video on convolutions: youtu.be/KuXjwB4LzSA
John Baez has a really fun article about this: johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail
Help fund future projects: patreon.com/3blue1brown
Special thanks to these patrons: 3b1b.co/lessons/borwein#thanks
An equally valuable form of support is to simply share the videos.
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
Hindi: Pragna1991
------------------
Original paper from David and Jonathan Borwein
https://carma.edu.au/resources/db90/pdfs/db90-119.00.pdf
Other fun coverage of the topic:
http://schmid-werren.ch/hanspeter/publications/2014elemath.pdf
johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail
Correction: 4:12 The top line should not be there, as that integral diverges
Timestamps
0:00 - The pattern
4:45 - Moving average analogy
10:41 - High-level overview of the connection
16:14 - What's coming up next
These animations are largely made using a custom python library, manim. See the FAQ comments here:
3blue1brown.com/faq#manim
github.com/3b1b/manim
github.com/ManimCommunity/manim
You can find code for specific videos and projects here:
github.com/3b1b/videos
Music by Vincent Rubinetti.
vincentrubinetti.com
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: 3blue1brown.com
Twitter: twitter.com/3blue1brown
Reddit: reddit.com/r/3blue1brown
Instagram: instagram.com/3blue1brown
Patreon: patreon.com/3blue1brown
Facebook: facebook.com/3blue1brown
A pattern of integrals that all equal pi...until they don't.
Next video on convolutions: youtu.be/KuXjwB4LzSA
John Baez has a really fun article about this: johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail
Help fund future projects: patreon.com/3blue1brown
Special thanks to these patrons: 3b1b.co/lessons/borwein#thanks
An equally valuable form of support is to simply share the videos.
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
Hindi: Pragna1991
------------------
Original paper from David and Jonathan Borwein
https://carma.edu.au/resources/db90/pdfs/db90-119.00.pdf
Other fun coverage of the topic:
http://schmid-werren.ch/hanspeter/publications/2014elemath.pdf
johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail
Correction: 4:12 The top line should not be there, as that integral diverges
Timestamps
0:00 - The pattern
4:45 - Moving average analogy
10:41 - High-level overview of the connection
16:14 - What's coming up next
These animations are largely made using a custom python library, manim. See the FAQ comments here:
3blue1brown.com/faq#manim
github.com/3b1b/manim
github.com/ManimCommunity/manim
You can find code for specific videos and projects here:
github.com/3b1b/videos
Music by Vincent Rubinetti.
vincentrubinetti.com
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: 3blue1brown.com
Twitter: twitter.com/3blue1brown
Reddit: reddit.com/r/3blue1brown
Instagram: instagram.com/3blue1brown
Patreon: patreon.com/3blue1brown
Facebook: facebook.com/3blue1brown
