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

02 Mar 2018 19:04 4,043
28,299 426

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:

Special thanks to patrons:

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.

Music by Vincent Rubinetti:


3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown

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