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A measure of axial symmetry of centrally symmetric convex bodies

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Lassak M., Nowicka M.

Colloquium Mathematicum

2010

tom 121

nr 2

295-306

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.

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1 Colloquium Mathematicum

1 Lassak M.

1 Nowicka M.

1 2010

Wyniki wyszukiwania

A measure of axial symmetry of centrally symmetric convex bodies