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. 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 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