Why is pi here? And why is it squared? A geometric answer to the Basel problem

A most beautiful proof of the Basel problem, using light.
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The content here was based on a paper by Johan Wästlund


Check out Mathologer's video on the many cousins of the Pythagorean theorem:


On the topic of Mathologer, he also has a nice video about the Basel problem:


A simple Geogebra to play around with the Inverse Pythagorean Theorem argument shown here.


Some of you may be concerned about the final step here where we said the circle approaches a line. What about all the lighthouses on the far end? Well, a more careful calculation will show that the contributions from those lights become more negligible. In fact, the contributions from almost all lights become negligible. For the ambitious among you, see this paper for full details.

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

Music by Vincent Rubinetti:


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