The stunning geometry behind this surprising equation
3,201
by Super User, 6 years ago
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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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
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/
------------------
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
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Super User uploaded a new media, The stunning geometry behind this surprising equation
6 years ago