Researchers thought this was a bug (Borwein integrals)
A pattern of integrals that all equal pi...until they don't.
Next video on convolutions: https://youtu.be/KuXjwB4LzSA
John Baez has a really fun article about this: https://johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail/
Help fund future projects: https://www.patreon.com/3blue1brown
Special thanks to these patrons: https://3b1b.co/lessons/borwein#thanks
An equally valuable form of support is to simply share the videos.
------------------
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
https://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:
https://www.3blue1brown.com/faq#manim
https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/
You can find code for specific videos and projects here:
https://github.com/3b1b/videos/
Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://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: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Видео Researchers thought this was a bug (Borwein integrals) канала 3Blue1Brown
Next video on convolutions: https://youtu.be/KuXjwB4LzSA
John Baez has a really fun article about this: https://johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail/
Help fund future projects: https://www.patreon.com/3blue1brown
Special thanks to these patrons: https://3b1b.co/lessons/borwein#thanks
An equally valuable form of support is to simply share the videos.
------------------
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
https://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:
https://www.3blue1brown.com/faq#manim
https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/
You can find code for specific videos and projects here:
https://github.com/3b1b/videos/
Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://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: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Видео Researchers thought this was a bug (Borwein integrals) канала 3Blue1Brown
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