Riemann zeta function

A 3D plot of the absolute value of the zeta function, highlighting some of its features. The red dots are the Riemann zeroes, and the pink plane is based at the critical line. The purple plane indicates the real axis.
See also
http://en.wikipedia.org/wiki/Riemann_hypothesis

Best when watched in high quality version.

This video is licensed under "Creative Commons Attribution-Share Alike 3.0 Unported License".

Category:

Science & Technology

Tags:

• mathematics
• riemann
• zeta
• function
• hypothesis
• conjecture
• zeroes

[Phoenix0886]

Wonderful! How have you realized it? Which program have you used? I'm going to graduate with a thesis on Riemann Zeta, and It would be fine to create a similar video...

[pdehaye]

sorry for the late reply. i used mathematica (for the first time), version 6. i used the Manipulate instruction to move the camera to positions i wanted, then used ListInterpolation to interpolate between those different points. this generated a series of images which i then animated using a stop motion program.

[zombierobopirate]

math is beautiful

[ortega24024]

It's easier to write your own programs than to use Mathematica (or whatever) sometimes! Hope your thesis went (or is going) OK. I did programmed zeta function graphics on an Amiga in 1993 - which ended up in a book in 2002.

[XxCHRISTIANxX2001]

whats the point of this?



[funChick84]

This is really amazing stuff, i hope to learn this material some day looks very challenging and exotic. Funny how i landed here i was reading about Gauss and scrolled down to find riemann now i cant stop watching all these videos. Ya i may not understand it but like i said someday maybe hopefully :)

[meatisdeliciouse]

The zeta function is amasing, I have tried to talk to my maths techeacher, excusse my spelling. Doesnt it also fit into DNA too? Maths is amasing, the only way we can comunicate with extra terestrials really.

[meatisdeliciouse]

This is so incredibly complicated, I cant even explain it to anyone. Didnt the find out that prime number directly corolate to the way atoms are built, if you translate them through the zeta function? I herd somewhere that the zeta function can even help to build the perfect amphithetre, I may be very inteligent, but how on earth do people actualy descover this, I mean it's so incredibly complicated, even I don't understand it all!!

[phicomingatya]

@Frisbieinstein There is reason for all zeros to be on 1/2 strip. It's because the prime zeta function has a singularity at s=1/2, which makes it possible for the zeta to have zeros on the line Re(s)=1/2.

[phicomingatya]

@monobrowperson lol, very funny!

[monobrowperson]

I found a zero that is not on the line. However, I also discovered an application to HAARP. Therefore, I won't disclose my secret. The Japanese will understand why.

[pdwu2]

@gae3tano The relation between the Rieman zeta function and primes is given by the Euler product formula, see wikipedia

[Frisbieinstein]

The function is purposefully constructed so that the zeros are the primes. That's not the mystery. Why are they all on the 1/2 strip? There seems to be no reason at all for that.

[gae3tano]

@pdehaye excuse me, but i don't undestand what are the real relations between the zero's on the critical line of rienmann hypotesys and prime numbers..there's somebody who can to explain that relations!??thancks