Researchers thought this was a bug (Borwein integrals)

A pattern of integrals that all equal pi...until they don't.
Next video on convolutions:    • But what is a convolution?  
John Baez has a really fun article about this: https://johncarlosbaez.wordpress.com/...

Help fund future projects:   / 3blue1brown  
Special thanks to these patrons: https://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/p...

Other fun coverage of the topic:
http://schmid-werren.ch/hanspeter/pub...

https://johncarlosbaez.wordpress.com/...

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/a...

Stream the music on Spotify:
https://open.spotify.com/album/1dVyjw...

------------------

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:   / 3blue1brown  
Reddit:   / 3blue1brown  
Instagram:   / 3blue1brown  
Patreon:   / 3blue1brown  
Facebook:   / 3blue1brown