Abstract

An old result of Zamfirescu says that for most convex curves C in the plane most points in R2 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 'continuum many' in the statement. We present further theorems in the same spirit.

Author information

Contact details are reproduced from the original publication and may be historical.

Imre Bárány

A. Rényi Mathematical Institute, Hungarian Academy of Sciences, PO Box 127, 1364 Budapest, Hungary

barany@renyi.hu

Miklós Laczkovich

Dept. of Analysis, Eötvös University, Pázány Péter Sétány 1/c, 1117 Budapest, Hungary

laczk@cs.elte.hu

Keywords

  • Convex curves in the plane
  • affine diameters
  • Baire category

Mathematics Subject Classification

52A10; 54E52

Suggested citation

I. Bárány, M. Laczkovich. “Magic Mirrors, Dense Diameters, Baire Category.” Journal of Convex Analysis 24 (2017), No. 1, 93–102.

Copyright Heldermann Verlag 2017