Magic mirrors, dense diameters, Baire category
arXiv:1403.0246
Abstract
An old result of Zamfirescu says that for most convex curves in the plane most points in lie on infinitely many normals to , where most is meant in Baire category sense. We strengthen this result by showing that `infinitely many' can be replaced by `contiunuum many' in the statement. We present further theorems in the same spirit.
10 pages, one figure