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

02 Mar 2018 19:04 4,043
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A most beautiful proof of the Basel problem, using light.
Plushie pi creatures now available: http://3b1b.co/store
More problem-driven learning: https://brilliant.org/3b1b

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

Special thanks to patrons:
https://www.patreon.com/3blue1brown
http://3b1b.co/basel-thanks

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

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.

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

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