Magic mirrors, dense diameters, Baire category
Metric Geometry
2014-03-04 v1
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.
Keywords
Cite
@article{arxiv.1403.0246,
title = {Magic mirrors, dense diameters, Baire category},
author = {Imre Bárány and Miklós Laczkovich},
journal= {arXiv preprint arXiv:1403.0246},
year = {2014}
}
Comments
10 pages, one figure