Visualizing the Riemann hypothesis and analytic continuation





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Published on Dec 9, 2016

Unraveling an enigmatic function.
Home page: https://www.3blue1brown.com/
Brought to you by you: http://3b1b.co/zeta-thanks
Posters/shirts for this visualization at http://3b1b.co/store

Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti...

Check out some of Vince's other work here: http://www.vincentrubinetti.com/

For those who want to learn more about complex exponentiation, here are a few resources:
- My video on the topic: http://youtu.be/mvmuCPvRoWQ
- Mathologer's: https://youtu.be/-dhHrg-KbJ0
- Better Explained: https://goo.gl/z28x2R

For those who want to learn more about the relationship between 1+2+3+4+... and -1/12, I'm quite fond of this blog post by Terry Tao: https://goo.gl/XRzyTJ

Also, in a different video "What does it feel like to invent math", I give a completely different example of how adding up growing positive numbers can meaningfully give a negative number, so long as you loosen your understanding of what distance should mean for numbers: https://youtu.be/XFDM1ip5HdU

Interestingly, that vertical line where the convergent portion of the function appears to abruptly stop corresponds to numbers whose real part is Euler's constant, ~0.577. For those who know what this is, it's kind of fun to puzzle about why this is the case.


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If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ

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