Spherical and ellipsoidality theorems for convex bodies
Dorn, C. (1978)
Portugaliae mathematica
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Dorn, C. (1978)
Portugaliae mathematica
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Fradelizi, Matthieu (1999)
Beiträge zur Algebra und Geometrie
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Makeev, V.V. (2005)
Journal of Mathematical Sciences (New York)
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Makeev, V.V. (2005)
Journal of Mathematical Sciences (New York)
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David G. Larman (2009)
Banach Center Publications
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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.
Lindquist, Norman F. (1975)
Portugaliae mathematica
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Zhang, Gaoyong (1999)
Annals of Mathematics. Second Series
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Groemer, H. (1993)
Beiträge zur Algebra und Geometrie
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Vojtěch Jarník (1948)
Časopis pro pěstování matematiky a fysiky
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Kramer, Horst (2006)
Mathematica Pannonica
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Brehm, Ulrich, Voigt, Jürgen (2000)
Beiträge zur Algebra und Geometrie
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Meckes, Mark W. (2009)
Beiträge zur Algebra und Geometrie
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Marek Lassak, Monika Nowicka (2010)
Colloquium Mathematicae
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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...