Magic mirrors, dense diameters, Baire category

zbMATH Open1366.52001arXiv1403.0246MaRDI QIDQ2974986

Publication date: 11 April 2017

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1403.0246

zbMATH Keywords

Baire category affine diameters convex curves in the plane

Mathematics Subject Classification ID

Baire category, Baire spaces (54E52) Convex sets in (2) dimensions (including convex curves) (52A10)

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