A most beautiful proof of the Basel problem, using light.
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The content here was based on a paper by Johan Wästlundhttp://www.math.chalmers.se/~wastlund...
Check out Mathologer's video on the many cousins of the Pythagorean theorem:https://youtu.be/p-0SOWbzUYI
On the topic of Mathologer, he also has a nice video about the Basel problem:https://youtu.be/yPl64xi_ZZA
A simple Geogebra to play around with the Inverse Pythagorean Theorem argument shown here.https://ggbm.at/yPExUf7b
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.
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Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/a...
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