A most beautiful proof of the Basel problem, using light.
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Special thanks to these supporters: http://3b1b.co/basel-thanks
This video was sponsored by Brilliant: https://brilliant.org/3b1b

Brilliant's principles list that I referenced:
https://brilliant.org/principles/

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The content here was based on a paper by Johan Wästlund
http://www.math.chalmers.se/~wastlund...

Check out Mathologer's video on the many cousins of the Pythagorean theorem:
   • Visualising Pythagoras: ultimate proo...  

On the topic of Mathologer, he also has a nice video about the Basel problem:
   • Euler's real identity NOT e to the i ...  

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.

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:
https://vincerubinetti.bandcamp.com/a...

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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