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How do convex bodies sit?
Published online by Cambridge University Press: 26 February 2010
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Every homogeneous convex body in ℝd (d≥2) put to sit on a horizontal hyperplane finds a position of stable equilibrium. A cube has 2d such positions and an ellipsoid with pairwise distinct axis-lengths has 2. How many positions of stable equilibrium have most convex bodies?
The term “most” is understood in the Baire category sense. For various other results on most convex bodies, see [2], [4].
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