I wrote, regarding a conformal map from the circle and its interior to an ellipse and its interior, taking the center to the center: << The vertices of a regular n-gon inscribed in the circle will be mapped to n vertices with the same angular separation along the ellipse (with respect to the its center).
This is not true. The radii of the circle ending at vertices of a regular n-gon inscribed in the circle will be taken to some curves from the center of the ellipse to the ellipse, and the curves will meet at equal angles, but that's all that can be said in this vein. * * * Question: Suppose we have an N-gon with all sides equal that's inscribed in an ellipse. Assume the sides rigid and the ellipse to be a track in which the vertices can slide. Under what conditions will this N-gon actually slide around the ellipse? --Dan Those who sleep faster get more rest.