On the disks with diameters the sides of a convex 5-gon
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چکیده
We prove that for any convex pentagon in the plane there are two disks, among the five disks having a side of the pentagon as diameter, that do not intersect. All our arguments are from classical Euclidean geometry.
منابع مشابه
The intersection graph of the disks with diameters the sides of a convex $n$-gon
Given a convex polygon of n sides, one can draw n disks (called side disks) where each disk has a different side of the polygon as diameter and the midpoint of the side as its center. The intersection graph of such disks is the undirected graph with vertices the n disks and two disks are adjacent if and only if they have a point in common. We prove that for every convex polygon this graph is pl...
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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 $k$ ...
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تاریخ انتشار 2014