A note on 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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Every row and column of the board has only two occupied squares. But if we also consider the diagonals with slope +1 or −1, we see that each of them contains either zero or two squares of the figure. We say that Figure 1 has constant width three by rows and columns, and that Figure 2 has constant width two by rows, columns, and diagonals. The first figure is easy to generalize in the sense that...
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Let tw(G), pw(G), c(G), !J.(G) denote, respectively, the tree-width, path-width, cutwidth and the maximum degree of a graph G on 11 vertices . It is known that c (G)~tw (G). We prove that c (G) =0 (tw (G)·!J.(G)·logn), and if ({Xj : iel] ,T=(I,A» is a tree decomposition of G with tree-wid~ then c (G) S (k+ l)·!J.(G)·c (T). In case that a tree decomposition is given, or that the tree-width is bo...
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P p(pi−1) , where the summation is over first N prime pi, k ∈ Z+. The classical summation formula is as follows: A = limN→∞Σ(N), where Σ(N) = 1 N ∑ φ(pi−1) pi−1 . The changes needed for arbitrary g are addressed in Theorem 1, a good exercise in basic analytic and algebraic number theory. The same procedure can be applied to other number-theoretic constants like A (see, e.g., [Ni]). In Theorem 2...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1960
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1960-0124814-5