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/

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Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
Hindi: Pragna1991

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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

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https://github.com/ManimCommunity/manim/

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