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.

  • $\begingroup$ Here is an MO thread you may find interesting. $\endgroup$ – user296602 Mar 3 '18 at 2:55

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.

  • $\begingroup$ Don't be sorry. It's great stuff. Have a nice day. $\endgroup$ – user357980 Mar 3 '18 at 3:05
  • $\begingroup$ "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: mathoverflow.net/a/178206/4678. $\endgroup$ – Hans Lundmark Mar 3 '18 at 8:46
  • $\begingroup$ @user357980: Wonderful reference. (+1) $\endgroup$ – Markus Scheuer Mar 3 '18 at 9:29

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