Stereographic projection of Riemann sphere

A video from the American Mathematical Society's Feature Column "Lorenz and Modular Flows: A Visual Introduction" by Etienne Ghys and Jos Leys, showing projections of the Riemann sphere. (Riemann is the person pictured.) See other cool videos by Ghys and Leys at http://www.ams.org/featurecolumn/archive/lorenz.html .

Category:

Science & Technology

Tags:

• math
• geometry
• Riemann
• stereographic
• projection
• Etienne
• Ghys
• Jos
• Leys

[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.

[birdieberry]

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

[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.

[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!

[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:')

[VERGIS92]

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

[UnlimitedMoops]

An animation :>)

[WonderWatcher1]

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

[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.