:Thanks for the tip about graphing. The usual way to construct conformal maps between polygons and a circle is using [http://en.wikipedia.org/wiki/Schwarz%E2%80%93Christoffel_mapping Schwartz-Christoffel mappings]. Unfortunately this is a bit of a pain to compute, but I think the square <-> circle example is a particularly nice one for people who have seen this before, and might not be too impressed by circle <-> upper half plane or other such. I'll take a look at your suggestions when I have a chance -- I think I may have tried to do this in mathematica once as well. Unfortunately I don't have upload rights to help you, but I'll keep at that talk page. | :Thanks for the tip about graphing. The usual way to construct conformal maps between polygons and a circle is using [http://en.wikipedia.org/wiki/Schwarz%E2%80%93Christoffel_mapping Schwartz-Christoffel mappings]. Unfortunately this is a bit of a pain to compute, but I think the square <-> circle example is a particularly nice one for people who have seen this before, and might not be too impressed by circle <-> upper half plane or other such. I'll take a look at your suggestions when I have a chance -- I think I may have tried to do this in mathematica once as well. Unfortunately I don't have upload rights to help you, but I'll keep at that talk page. |