The stunning geometry behind this surprising equation

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by Super User, 5 months ago
0 0
A most beautiful proof of the Basel problem, using light.
More problem-driven learning: https://brilliant.org/3b1b

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

Content like this is made possible by the very kind subset of you who choose to contribute for each new video:
http://3b1b.co/support

Special thanks to these Patrons:
http://3b1b.co/basel-thanks

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

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

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.

Music by Vincent Rubinetti:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
https://soundcloud.com/vincerubinetti/

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