Researchers thought this was a bug (Borwein integrals)

2022-11-04

[public] 265K views, 84.7K likes, dislikes audio only

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A pattern of integrals that all equal pi...until they don't.

Next video on convolutions: /youtube/video/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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