Convex bodies of constant width and constant brightness
نویسندگان
چکیده
منابع مشابه
Nakajima’s Problem: Convex Bodies of Constant Width and Constant Brightness
For a convex body K ⊂ Rn, the kth projection function of K assigns to any k-dimensional linear subspace of Rn the k-volume of the orthogonal projection of K to that subspace. Let K and K0 be convex bodies in Rn, and let K0 be centrally symmetric and satisfy a weak regularity and curvature condition (which includes all K0 with ∂K0 of class C2 with positive radii of curvature). Assume that K and ...
متن کاملConvex Bodies of Constant Width and Constant Brightness
Under the extra assumption that the boundary is of class C this was proven by S. Nakajima (= A. Matsumura) in 1926 Theorem 1 solves this problem. For convex bodies with C boundaries and positive curvature Nakajima’s result was generalized by Chakerian [?] in 1967 to “relative geometry” where the width and brightness are measured with with respect to some convex body K0 symmetric about the origi...
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The study of constant width sets goes at least as far back as the time of Euler. The Apollonian metric, on the other hand, is a relatively new concept. It was introduced by Beardon in 1998 as a generalization of the hyperbolic metric of a ball to arbitrary domains [3]. Close connections between these concepts were established in [20] and [21]. In this paper, we study the Apollonian metric of do...
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A bounded convex set has constant width d iff any two parallel (and nonidentical) tangent planes to it have identical distance d from each other. Clearly balls have this property, but there are also other sets of constant width. This lecture was originally designed for a general audience as part of a series of lectures during the German “Year of Mathematics” 2008. It starts by presenting eviden...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2006
ISSN: 0001-8708
DOI: 10.1016/j.aim.2005.05.015