Axially Symmetric Polygons Inscribed in and Circumscribed about Convex sets.
B. de Abel de Valcourt (1967)
Elemente der Mathematik
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B. de Abel de Valcourt (1967)
Elemente der Mathematik
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Peter McCullen (1976)
Elemente der Mathematik
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Lassak, Marek, Nowicka, Monika (2009)
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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...
G.D. Chakerian (1963)
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