A measure of axial symmetry of centrally symmetric convex bodies

• Autorzy: Marek Lassak , Monika Nowicka
• Języki publikacji: EN

Abstrakty

EN

Denote by Kₘ the mirror image of a planar convex body K in a straight line m. It is easy to show that K*ₘ = conv(K ∪ Kₘ) is the smallest by inclusion convex body whose axis of symmetry is m and which contains K. The ratio axs(K) of the area of K to the minimum area of K*ₘ over all straight lines m is a measure of axial symmetry of K. We prove that axs(K) > 1/2√2 for every centrally symmetric convex body and that this estimate cannot be improved in general. We also give a formula for axs(P) for every parallelogram P.

Kategorie tematyczne

• 52A10: Convex sets in 2 dimensions (including convex curves)
• 52A38: Length, area, volume

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 121
• Numer: 2
• Strony: 295-306

Daty

wydano

2010

Twórcy

autor

Marek Lassak

• Institute of Mathematics and Physics, University of Technology, 85-796 Bydgoszcz, Poland

autor

Monika Nowicka

• Institute of Mathematics and Physics, University of Technology, 85-796 Bydgoszcz, Poland

Identyfikatory

DOI

10.4064/cm121-2-12