Are there any visual proofs for $\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$?

I was flipping through Proofs Without Words (PWW) and saw many visual proofs for sequences and series. However, I saw none for $$\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$$

Are there any visual proofs for the above series?

Solution 1:

In his extraordinary paper, Mikael Passare presents following visual idea:

Even more amazing than the above picture are techniques used for the proof. They involve basic math only, essentially trigonometry and more visual transformations of curved (sometimes infinite!) and straight line areas, like this one:

Here all six region have the same area, check the details in the paper.

Solution 2:

Grant Sanderson just published a video on his channel 3Blue1Brown in which he presents a very accessible way of visualizing the problem and its solution. Link to the video:

https://youtu.be/d-o3eB9sfls