[pipingdog]

If you want to get a flavor of the article without being too much of a math person, you can watch the 3Blue1Brown video linked in the article, which captures a similar surprise that for certain values a formula maps exactly to a "round" quantity, then starts to diverge after a while.

https://www.youtube.com/watch?v=851U557j6HE

[schlauerfox]

My ignorant intuition is since it's the area between sin(x)/x and the x axis, but as you get further into infinity the 1/x still keeps getting smaller slowly but sin(x) always is the same magnitude, the integral gets slightly further away the closer you get to infinity and that slight difference adds up?

[hgsgm]

Yes but the question is why the value is exact for small N.

[kragen]

that borwein integral formula is one of the first things baez mentions

[tiagod]

The comment you replied to mentions that the video is linked in the article.

[kragen]

so it does, i'm an idiot, thanks