Is there any geometry behind the Basel problem?

Question

I could find many beautiful and rigorous proofs for Euler's solution to the Basel problem here Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem)

Basel problem solution

But I am curious to know whether there are proofs by using geometry.

If anyone has proofs by geometry, please do share it with us.

Here is an MO thread you may find interesting. – Mar 03 '18 at 02:55 — , Mar 03 '18 at 02:55

score 2 · Accepted Answer · answered Mar 03 '18 at 03:01

2

Funny you should ask this today. A great video video by the YouTuber 3Blue1Brown was just posted today. (Aside: I recommend all his videos.)

The proof is based on the result mentioned by "3 revs" in the MO thread mentioned by user296602 above.

answered Mar 03 '18 at 03:01

user357980

Don't be sorry. It's great stuff. Have a nice day. – user357980 Mar 03 '18 at 03:05
"3 revs" is not a user, it means "3 revisions" (of a community wiki post). A better identifier is obtained by clicking "share", which gives you a direct link to that answer: https://mathoverflow.net/a/178206/4678. – Hans Lundmark Mar 03 '18 at 08:46
@user357980: Wonderful reference. (+1) – Markus Scheuer Mar 03 '18 at 09:29

1 Answers1