Combinatorial Geometry
نویسندگان
چکیده
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 Newton, Gauss, Minkowski, and Hilbert, as well as new areas of investigation. The textbooks by Matousek [12] and, Pach and Agarwal [15] provide an overview of the topics and methods.
منابع مشابه
A 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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