English

Magic mirrors, dense diameters, Baire category

Metric Geometry 2014-03-04 v1

Abstract

An old result of Zamfirescu says that for most convex curves CC in the plane most points in R2R^2 lie on infinitely many normals to CC, 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

R2 v1 2026-06-22T03:18:39.312Z