Researchers thought this was a bug (Borwein integrals)
A curious pattern of integrals that all equal pi...until they don't.
This is the first of two videos exploring a somewhat mind-blowing pattern of integrals. The next video will be all about convolutions, filling in the details not fully explained here, as well as showing where else convolutions come up in math.
Might it have something to do with (12+1) and (36+1)x3 being cool integers ? I have this crush lately with both, because you see "the mathematical phase transition" happening near them in so many different contexts.
I always made a lot of tricks to understand the sliding window when doing convolutions. Also the relation between product and convolution being trans-domain equivalent was always something I cherished, and found really useful and inspiring. Can't wait to see how you follow this up. Thank you so much!