Geodesic
Magic Mirrors, Dense Diameters, Baire Category
Journal of convex analysis, Tome 24 (2017) no. 1, pp. 93-102
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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.
Classification : 52A10, 54E52
Mots-clés : Convex curves in the plane, affine diameters, Baire category 
@article{JCA_2017_24_1_JCA_2017_24_1_a6,
     author = {I. B\'ar\'any and M. Laczkovich},
     title = {Magic {Mirrors,} {Dense} {Diameters,} {Baire} {Category}},
     journal = {Journal of convex analysis},
     pages = {93--102},
     year = {2017},
     volume = {24},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a6/}
}
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I. Bárány; M. Laczkovich. Magic Mirrors, Dense Diameters, Baire Category. Journal of convex analysis, Tome 24 (2017) no. 1, pp. 93-102. http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a6/