Sets of constant width
نویسندگان
چکیده
منابع مشابه
Convex sets of constant width
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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PETER HÄSTÖ, ZAIR IBRAGIMOV AND DAVID MINDA ABSTRACT. In this article we study -diameter of planar sets of constant width. We obtain analogues of the isodiametric inequality and the Blaschke-Lebesgue Theorem for -diameter of constant width sets. Namely, we prove that among all the sets of given constant width, disks have the smallest -diameter and Reuleaux triangles have the largest -diameter. ...
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A subset of the d-dimensional Euclidean space having nonempty interior is called a spindle convex body if it is the intersection of (finitely or infinitely many) congruent d-dimensional closed balls. The spindle convex body is called a “fat” one, if it contains the centers of its generating balls. The core part of this paper is an extension of Schramm’s theorem and its proof on illuminating con...
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A pplications written for the embedded domain must perform under the constraints of limited memory and limited energy. While these constraints have always existed, current trends, such as mobile computing and ubiquitous computing, bring more and more complex applications to the embedded domain, making performance, or speed of execution, an important factor as well. For instance, we are now able...
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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 ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1966
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1966.19.13