منابع مشابه
Numerical range circumscribed by two polygons
We show that, for any 2n+ 2 distinct points a1, a′ 1, a2, a′ 2, . . . , an+1, a′ n+1 (in this order) on the unit circle, there is an n-by-n matrix A, unique up to unitary equivalence, which has norm one and satisfies the conditions that it has all its eigenvalues in the open unit disc, In − A∗A has rank one and its numerical range is circumscribed by the two (n+ 1)-gons a1a2 · · · an+1 and a′ 1...
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From the pentagon onwards, the area of the regular convex polygon with n sides and unit diameter is greater for each odd number n than for the next even number n + 1. Moreover, from the heptagon onwards, the difference in areas decreases when n increases. Similar properties hold for the perimeter. A new proof of a result of Reinhardt follows.
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We describe the first-order variations of the angles of Euclidean, spherical or hyperbolic polygons under infinitesimal deformations such that the lengths of the edges do not change. Using this description, we introduce a vector-valued quadratic invariant b on the space of those isometric deformations which, for convex polygons, has a remarkable positivity property. We give two geometric applic...
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Abstract. Sequences of polygons generated by performing iterative processes on an initial polygon have been studied extensively. One of the most popular sequences is the one sometimes referred to as Kasner polygons. Given a polygon K, the first Kasner descendant K ′ of K is obtained by placing the vertices of K ′ at the midpoints of the edges of K. More generally, for any fixed m in (0, 1) one ...
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We say that a polygon inscribed in the circle is asymmetric if it contains no two antipodal points being the endpoints of a diameter. Given n diameters of a circle and a positive integer k < n, this paper addresses the problem of computing a maximum area asymmetric k-gon having as vertices k < n endpoints of the given diameters. The study of this type of polygons is motivated by ethnomusiciolog...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2008
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-008-9072-z