Magic mirrors, dense diameters, Baire category
  An old result of Zamfirescu says that for most convex curves $C$ in the plane most points in $R^2$ lie on infinitely many normals to $C$, 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. 
Imre B\'ar\'any and Mikl\'os Laczkovich
math.MG