منابع مشابه
An Isoperimetric Theorem in Plane Geometry
An isoperimetric theorem in plane geometry Alan Siegel1 COURANT INSTITUTE OF MATHEMATICAL SCIENCES NEW YORK UNIVERSITY New York Abstract Let be a simple polygon. Let the vertices of be mapped, according to a counterclockwise traversal of the boundary, into a strictly increasing sequence of real numbers in . Let a ray be drawn from each vertex so that the angle formed by the ray and a horizontal...
متن کاملA convex combinatorial property of compact sets in the plane and its roots in lattice theory
K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...
متن کاملA combinatorial problem in geometry
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متن کاملCombinatorial optimization in geometry
In this paper we extend and unify the results of [20] and [19]. As a consequence, the results of [20] are generalized from the framework of ideal polyhedra in H to that of singular Euclidean structures on surfaces, possibly with an infinite number of singularities (by contrast, the results of [20] can be viewed as applying to the case of non-singular structures on the disk, with a finite number...
متن کاملCombinatorial Geometry
Combinatorial geometry is the study of combinatorial properties of fundamental geometric objects, whose origins go back to antiquity. It has come into maturity in the last century through the seminal works of O. Helly, K. Borsuk, P. Erdős, H. Hadwidger, L. Fejes Tóth, B. Grübaum and many other excellent mathematicians who initiated new combinatorial approaches to classical questions studied by ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1975
ISSN: 0095-8956
DOI: 10.1016/0095-8956(75)90061-1