Is it possible to build a metal wire sphere whose shadow projects the 2d conformal maps of the Riemann Sphere on a flat wall? Is it possible to build a metal wire hollow sphere whose shadow from a nearby point light source projects the 2d conformal maps of the Riemann Sphere on a flat wall?
I believe that in theory it should be possible, but I was not sure if there would be any physical impracticabilities that would limit such a shadow project.

This can be done.  For example, see
https://www.shapeways.com/model/1480313/grid-stereographic-projection.html
The technical name for this way of "casting shadows" is called stereographic projection.  See


*

*https://www.youtube.com/watch?v=0z1fIsUNhO4

*https://www.youtube.com/watch?v=6JgGKViQzbc

*http://en.wikipedia.org/wiki/Stereographic_projection

*http://mathworld.wolfram.com/StereographicProjection.html

*http://www.ams.org/samplings/feature-column/fc-2014-02
and so on. 
