Find the natural number
with the following properties:
Let
be an arbitrary finite set of points in the plane, and
the distance from
to the origin
We assign to each
the closed disk
with center
and radius
. Then some
of these disks contain all points of
is the smallest integer with the above property.
%V0
$(SWE 3)$ Find the natural number $n$ with the following properties:
$(1)$ Let $S = \{P_1, P_2, \cdots\}$ be an arbitrary finite set of points in the plane, and $r_j$ the distance from $P_j$ to the origin $O.$ We assign to each $P_j$ the closed disk $D_j$ with center $P_j$ and radius $r_j$. Then some $n$ of these disks contain all points of $S.$
$(2)$ $n$ is the smallest integer with the above property.
Školjka