Stereographic projection of Riemann sphere

[TetrahedronInSphere]

It would be interesting to add walls and ceiling to the projection

[leaq]

thanks so much for this! i was trying desperately to picture it in my head but failing. one thing you could perhaps do if you were looking to improve it would be to show how circles on the Riemann sphere going through the north pole N correspond to LINES on the extended complex plane (although I managed to intuit this from your excellent display anyway). again, thanks very much!

[VERGIS92]

Rieman is great example of german intellect, and the father of relativistic geometry, without it there would no be Einstein and G.R.

[WonderWatcher1]

If this is projecting 3d onto a 2d plane, what would projecting a 4d onto a 3d space look like?

[UnlimitedMoops]

An animation :>)

[RealizedPotential]

@WonderWatcher1 When I think of 4d, I think of 3d plus time. So I thinks 4d in 3d could thought of as a 3d movie. But I could be complete wrong:')

[arjunmax7]

great

[ilanpi]

This projection was already known to the Ancient Greeks 2000 years before Riemann, it is the basis of the astrolabe from the Middle Ages.

[cheezmunky]

This is the devil.

[tinnigeimgengill]

cool

[jamextv]

Hi! very nice your work. I´being trying to do this kind of projection in 3dmax but I can´t seem to find the exact procidure. Is there any way to get any hints of what do I have to do(or in what program do I have to do it, I was thinking that perhaps in maya or combustion)

Thanks and congrats! ;)

[mikeabreen]

@jamextv You can contact the creators of the video and see more of their work at ams.org/samplings/feature-colu­mn/fcarc-lorenz.

[jamextv]

Thanks man! I'll try to contact them

[Ajm4756]

Fz = Az +B / Cz + D

[dannyboy12357]

cute

[iceyflames7]

wat the guy said below me is that small image goes in ball bigger one comes out and he messures how big it will get.

[seahyimin]

is this supposed to be a system to convert far-away coordinates into smaller coordinates by finding the coordinate on the sphere formed by the line joining the top of the sphere and the xy plane?

[azkeyz]

I'd say this video demonstrates ALOT

I won't breath a word of what I see to anyone , I'm in competition to solve remanns , I believe I've solved it and of course can't tell anyone what so ever except qualified personel.

I won't say good luck because I'm not a lucifarian , I'm a judeochristian so I'll say may divine providence be apon you.

[TheLastCoolName]

What

[NexIuguolo]

hey i herd you liek mudkipz

[FreeInquisition]

lol

[demonstorm2012]

allmost like a shadow

[jrs89]

What does this have to do with anything?

[pwiattitto]

erm... what's this got to do with stereographics? stereographics are those pictures/video which reveals it's depth when looking at them with crossed eyes, right?

[slappy480ic3f4]

are those rays supposed to be orthogonal?

[joelito101]

I'm going to make one of those spheres with an image on it, I want to see it.

[kablay1]

Wut wuz that?

[MontalvoCantu]

you have to se moebius tranformation video first to understand this one

[Mazmatickz]

Riemann is awesome^^ One of the greatest mathematicians ever lived!

[mattmartmale]

Are there any videos that show what the projection looks like when it completely flips? like what it would look like if there was another plane above the sphere?

[helenagunther]

Yes, take a look at "Moebius Transformations Revealed". It explains a lot.

[dibbuck]

nyce

[MarthaMartian]

Looks very interesting. I seem to understand. Mostly it reminds me of a video needing music to match it. "The Riemann Sphere" by Tom Waits? I will study this video model more and come back with a better grasp of this.

[materiasacra]

The interesting thing is that it shows that the plane can be 'compactified' by adding just one point. This extra point is the top of the sphere. It corresponds to 'infinity' in the plane. You might think that a plane has many different 'infinities', because you can move further and further away in any direction. But the direction does not really matter. The projection always ends up at the top of the sphere. This shows that adding a single point suffices to turn the plane into a compact set.

[pkt171]

thanks, materia, for your single point about the single point. it helped me see the compactification of the plane. incidentally, the sphere IS a parametrization, no?

[materiasacra]

Yes. To be slightly more precise: coordinates describing points on the sphere (e.g. azimuth and polar angles) are a parametrization of the plane, the top point of the sphere being excluded.

[ler0np0]

I think this is certain solid angle of a sphere subtending certain area of a plane at different angles and distances.

[mayormcch33z]

I don't understand. It's just a sphere with a light in it projecting a picture onto a plane, right?

[ErkDemon]

Yep, but the projection is fascinating: it illustrates how a finite, curved, closed surface can be projected onto an infinite undistorted plane.

The mapping was interesting to cosmologists after Einstein introduced his general theory of relativity, because it showed how the geometrical relationships could be transferred between an infinite, "flat" universe and a closed hyperspherical one (as long as the critical distances were all transformed correctly).

[waparker4]

RE: ErkDemon. To project the sphere onto the plane, it is necessary that one point be removed, usually and in this case the north pole. Thus it is not a completely closed surface.

[birdieberry]

LOL to use a picture of the mathematician to demonstrate his theory--brilliant! ;D