Visualizing the Riemann zeta function and analytic continuation
Unraveling the enigmatic function behind the Riemann hypothesis
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/zeta-thanks
Home page: https://www.3blue1brown.com/
Posters/shirts for this visualization at http://3b1b.co/store
Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti/riemann-zeta-function
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.
------------------
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 about 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: https://goo.gl/WmnCQZ
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
Видео Visualizing the Riemann zeta function and analytic continuation канала 3Blue1Brown
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/zeta-thanks
Home page: https://www.3blue1brown.com/
Posters/shirts for this visualization at http://3b1b.co/store
Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti/riemann-zeta-function
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.
------------------
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 about 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: https://goo.gl/WmnCQZ
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
Видео Visualizing the Riemann zeta function and analytic continuation канала 3Blue1Brown
Показать
Комментарии отсутствуют
Информация о видео
Другие видео канала
Pi hiding in prime regularitiesRamanujan: Making sense of 1+2+3+... = -1/12 and Co.Why -1/12 is a gold nuggetWhat is the Riemann Hypothesis?Thinking outside the 10-dimensional boxBut how does bitcoin actually work?[Visual] The Riemann Zeta Function VisualisedWhy is pi here? And why is it squared? A geometric answer to the Basel problemFractals are typically not self-similarBarry Mazur "A Lecture on Primes and the Riemann Hypothesis" [2014]The unexpectedly hard windmill question (2011 IMO, Q2)The Key to the Riemann Hypothesis - NumberphileEuler's formula with introductory group theoryBut what is the Fourier Transform? A visual introduction.Why do prime numbers make these spirals? | Dirichlet’s theoremThe other way to visualize derivatives | Chapter 2, Essence of calculusYes -1/12 (with an integral)Who cares about topology? (Inscribed rectangle problem)Visualizing quaternions (4d numbers) with stereographic projection