The determination of convex bodies from the size and shape of their projections and sections

Paul Goodey

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Displaying similar documents to “The determination of convex bodies from the size and shape of their projections and sections”

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A measure of axial symmetry of centrally symmetric convex bodies

Marek Lassak, Monika Nowicka (2010)

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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...

The skeleta of convex bodies

David G. Larman (2009)

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The connectivity and measure theoretic properties of the skeleta of convex bodies in Euclidean space are discussed, together with some long standing problems and recent results.