I know that Geogebra 3D is not ready, but I couldn’t resist downloading to try it out in a class I am taking here at the University of Nebraska Lincoln. We are talking about Riemann spheres and stereographic projections with the complex plain. Cool stuff, but the book was no help in visualizing this so I knew it would be worth the risk to download. This program will be amazing when it is released officially. The only thing I wish it had was a simple way to intersect two three dimensional objects. I am sure it is possible, but have yet to see how it is done.
In the image above I show the set Z of all points of projection for a line that does not pass through the origin on the complex plane. In the program as you pull point A out to infinity, it is possible to watch the intersection circle Z get smaller as it approaches the pole of the sphere at point N. Sorry to not clean up my description mathematically, but just to excited and thought I needed to share the amazing fact that this problem which was hard to visualize was like putty in my hands with this program. Great job Markus and the Geogebra Team!!! Can’t wait for the official release.
Here is a copy of my write up for that problem. Have not had much time to clean it up, but Geogebra makes for a nice presentation Schaben Riemann Spheres Stereographic Projection